Select the appropriate word to complete each of the following.

Every positive number has ______ square root(s).

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

The principal square root is never ______.

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

For any ____ number $a,$ we have $\sqrt{a^{2}}=a$

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

For any ______ number $a,$ we have $\sqrt{a^{2}}=-a$

Check back soon!

Select the appropriate word to complete each of the following.

If $a$ is a whole number that is not a perfect square, then $\sqrt{a}$ is a(n) ______ number.

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

The domain of the function $f$ given by $f(x)=\sqrt[3]{x}$ is the set of all ______ numbers..

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

If $\sqrt[4]{x}$ is a real number, then $x$ must be ________.

Cory K.

Numerade Educator

Select the appropriate word to complete each of the following.

If $\sqrt[3]{x}$ is negative, then $x$ must be _____.

Cory K.

Numerade Educator

Identify the radicand and the index for each expression.

$$

5 \sqrt{p^{2}}+4

$$

Cory K.

Numerade Educator

Identify the radicand and the index for each expression.

$$

-7 \sqrt{y^{2}}-8

$$

Cory K.

Numerade Educator

Identify the radicand and the index for each expression.

$$

x y \sqrt[5]{\frac{x}{y+4}}

$$

Cory K.

Numerade Educator

Identify the radicand and the index for each expression.

$$

\frac{a}{b} \sqrt[6]{a^{2}+1}

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

f(t)=\sqrt{5 t-10} ; f(3), f(2), f(1), f(-1)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

g(x)=\sqrt{x^{2}-25} ; g(-6), g(3), g(6), g(13)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

t(x)=-\sqrt{2 x^{2}-1} ; t(5), t(0), t(-1), t\left(-\frac{1}{2}\right)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

p(z)=\sqrt{2 z-20} ; p(4), p(10), p(12), p(0)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

f(t)=\sqrt{t^{2}+1} ; f(0), f(-1), f(-10)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

g(x)=-\sqrt{(x+1)^{2}} ; g(-3), g(4), g(-5)

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{64 x^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{25 t^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{(-4 b)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{(-7 c)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{(8-t)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{(a+3)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{y^{2}+16 y+64}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{x^{2}-4 x+4}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{4 x^{2}+28 x+49}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{9 x^{2}-30 x+25}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

-\sqrt[4]{256}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

-\sqrt[4]{625}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[5]{-1}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

-\sqrt[3]{-1000}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

-\sqrt[5]{-\frac{32}{243}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[5]{-\frac{1}{32}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[6]{x^{6}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[8]{y^{8}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[9]{t^{9}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[5]{a^{5}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[4]{(6 a)^{4}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[4]{(8 y)^{4}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[10]{(-6)^{10}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[12]{(-10)^{12}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[414]{(a+b)^{414}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt[1976]{(2 a+b)^{1976}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{a^{22}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{x^{10}}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{-25}

$$

Cory K.

Numerade Educator

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.

$$

\sqrt{-16}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{16 x^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{25 t^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt{(3 t)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt{(7 c)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{(a+1)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{(5+b)^{2}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{9 t^{2}-12 t+4}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{25 t^{2}-20 t+4}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt[3]{27 a^{3}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt[3]{64 y^{3}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt[4]{16 x^{4}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt[4]{81 x^{4}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt[5]{(x-1)^{5}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt[7]{(1-x)^{7}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt[3]{-125 y^{3}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

-\sqrt[3]{-64 x^{3}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{t^{18}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{a^{14}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{(x-2)^{8}}

$$

Cory K.

Numerade Educator

Simplify. Assume that no radicands were formed by raising negative quantities to even powers.

$$

\sqrt{(x+3)^{10}}

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

f(x)=\sqrt[3]{x+1} ; f(7), f(26), f(-9), f(-65)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

g(x)=-\sqrt[3]{2 x-1} ; g(0), g(-62), g(-13), g(63)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

g(t)=\sqrt[4]{t-3} ; g(19), g(-13), g(1), g(84)

$$

Cory K.

Numerade Educator

For each function, find the specified function value, if it exists. If it does not exist, state this.

$$

f(t)=\sqrt[4]{t+1} ; f(0), f(15), f(-82), f(80)

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

f(x)=\sqrt{x-6}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

g(x)=\sqrt{x+8}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

g(t)=\sqrt[4]{t+8}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

f(x)=\sqrt[4]{x-9}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

g(x)=\sqrt[4]{2 x-10}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

g(t)=\sqrt[3]{2 t-6}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

f(t)=\sqrt[5]{8-3 t}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

f(t)=\sqrt[6]{4-3 t}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

h(z)=-\sqrt[6]{5 z+2}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

d(x)=-\sqrt[4]{7 x-5}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

f(t)=7+\sqrt[8]{t^{8}}

$$

Cory K.

Numerade Educator

Determine the domain of each function described.

$$

g(t)=9+\sqrt[6]{t^{6}}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

f(x)=\sqrt{5-x}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

g(x)=\sqrt{2 x+1}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

f(x)=1-\sqrt{x+1}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

g(x)=2+\sqrt{3 x-5}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

g(x)=3+\sqrt{x^{2}+4}

$$

Cory K.

Numerade Educator

Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range.

$$

f(x)=5-\sqrt{3 x^{2}+1}

$$

Cory K.

Numerade Educator

Match each function with one of the following graphs without using a calculator.

(GRAPH CAN'T COPY)

$$

f(x)=\sqrt{x-4}

$$

Cory K.

Numerade Educator

Match each function with one of the following graphs without using a calculator.

(GRAPH CAN'T COPY)

$$

g(x)=\sqrt{x+4}

$$

Cory K.

Numerade Educator

Match each function with one of the following graphs without using a calculator.

(GRAPH CAN'T COPY)

$$

h(x)=\sqrt{x^{2}+4}

$$

Cory K.

Numerade Educator

Match each function with one of the following graphs without using a calculator.

(GRAPH CAN'T COPY)

$$

f(x)=-\sqrt{x-4}

$$

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

The table below lists the average salary of a major-league baseball player, based on the number of years in his contract.

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

The number of gallons per minute discharged from a fire hose depends on the diameter of the hose and the nozzle pressure. The table below lists the amount of water flow for a 2 -in. diameter solid bore nozzle at various nozzle

pressures.

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

Koi, a popular fish for backyard pools, grow from $\frac{1}{40} \mathrm{cm}$ when newly hatched to an average length of $80 \mathrm{cm} .$ The table below lists the length of a koi at various ages.

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

The table below lists the average size of United States' farms for various years from 1960 to 2007

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

The table below lists the amount of federal funds allotted to the National Cancer Institute for cancer research in the United States from 2005 to 2010.

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Determine whether a radical function would be a good model of the given situation.

The table below lists the percent of households with basic cable television service for various years.

(TABLE CAN'T COPY)

Cory K.

Numerade Educator

Firefighting. The water flow, in number of gallons per minute (GPM), for a 2 -in. diameter solid bore nozzle is given by

$$

f(x)=118.8 \sqrt{x}

$$

where $x$ is the nozzle pressure, in pounds per square inch (psi). (See Exercise $116 .$ ) Use the function to estimate the water flow when the nozzle pressure is 50 psi and when it is 175 psi.

Cory K.

Numerade Educator

Koi Growth. The length, in centimeters, of a koi of age $x$ months can be estimated using the function

$$

f(x)=0.27+\sqrt{71.94 x-164.41}

$$

(See Exercise $117 .$ ) Use the function to estimate the length of a koi at 8 months and at 20 months.

Cory K.

Numerade Educator

Explain how to write the negative square root of a number using radical notation.

Cory K.

Numerade Educator

Does the square root of a number's absolute value always exist? Why or why not?

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$\left(a^{2} b\right)\left(a^{4} b\right)$$

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$

\left(3 x y^{8}\right)\left(5 x^{2} y\right)

$$

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$

\left(5 x^{2} y^{-3}\right)^{3}

$$

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$

\left(2 a^{-1} b^{2} c\right)^{-3}

$$

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$

\left(\frac{10 x^{-1} y^{5}}{5 x^{2} y^{-1}}\right)^{-1}

$$

Cory K.

Numerade Educator

Simplify. Do not use negative exponents in your answer.

$$

\left(\frac{8 x^{3} y^{-2}}{2 x z^{4}}\right)^{-2}

$$

Cory K.

Numerade Educator

If the domain of $f=[1, \infty)$ and the range of $f=[2, \infty),$ find a possible expression for $f(x)$ and explain how such an expression is formulated.

Cory K.

Numerade Educator

Natasha obtains the following graph of

$$

f(x)=\sqrt{x^{2}-4 x-12}

$$

and concludes that the domain of $f$ is $(-\infty,-2]$ Is she correct? If not, what mistake is she making?

(GRAPH CAN'T COPY)

Cory K.

Numerade Educator

Could the following situation possibly be modeled using a radical function? Why or why not? "For each year, the yield increases. The amount of increase is smaller each year."

Cory K.

Numerade Educator

Could the following situation possibly be modeled using a radical function? Why or why not? "For each year, the costs increase. The amount of increase is the same each year."

Cory K.

Numerade Educator

A parking lot has attendants to park the cars. The number $N$ of stalls needed for waiting cars before attendants can get to them is given by the formula $N=2.5 \sqrt{A},$ where $A$ is the number of arrivals in peak hours. Find the number of spaces needed for the given number of arrivals in peak hours:

(a) $25 ;$ (b) $36 ;(c) 49 ;$ (d) 64

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

$$

g(x)=\sqrt{x}+5

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

$$

f(x)=\sqrt{x+5}

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

$$

f(x)=\sqrt{x-2}

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

$$

g(x)=\sqrt{x}-2

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

Find the domain of $f$ if

$$

f(x)=\frac{\sqrt{x+3}}{\sqrt[4]{2-x}}

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

Find the domain of $g$ if

$$

g(x)=\frac{\sqrt[4]{5-x}}{\sqrt[6]{x+4}}

$$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

Find the domain of $F$ if $F(x)=\frac{x}{\sqrt{x^{2}-5 x-6}}$

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

Examine the graph of the data in Exercise $119 .$ What type of function could be used to model the data?

Cory K.

Numerade Educator

Determine the domain of each function described. Then draw the graph of each function.

In Exercise $120,$ a radical function could be used to model the data through $2000 .$ What might have caused the number of basic cable subscribers to change its pattern of growth?

Cory K.

Numerade Educator