Section 1
Radical Expressions
Simplify each rational expression.$\frac{x^2+7 x+12}{x^2-16}$
Simplify each rational expression.$\frac{a^3-b^3}{b^2-a^2}$
Perform the operations.$\frac{x^2-x-6}{x^2-2 x-3} \cdot \frac{x^2-1}{x^2+x-2}$
Perform the operations.$\frac{x^2-3 x-4}{x^2-5 x+6} \div \frac{x^2-2 x-3}{x^2-x-2}$
Perform the operations.$\frac{3}{m+1}+\frac{3 m}{m-1}$
Perform the operations.$\frac{2 x+3}{3 x-1}-\frac{x-4}{2 x+1}$
Fill in the blanks.7. $5 x^2$ is the square root of $25 x^4$, because __________ $=25 x^4$.
Fill in the blanks.6 is a square root of 36 because __________
Fill in the blanks.The principal square root of $x(x>0)$ is the __________ square root of $x$.
Fill in the blanks.$\sqrt{x^2}=$ __________
Fill in the blanks.The graph of $f(x)=\sqrt{x}+3$ is the graph of $f(x)=\sqrt{x}$ translated ____ units _________
Fill in the blanks.The graph of $f(x)=\sqrt{x+5}$ is the graph of $f(x)=\sqrt{x}$ translated ____ units to the _________
Fill in the blanks.$(\sqrt[3]{x})^3=$ _________
Fill in the blanks.$\sqrt[3]{x^3}=-$ _________
Fill in the blanks.When $n$ is an odd number greater than $1, \sqrt[n]{x}$ represents an _________ root.
Fill in the blanks.When $n$ is a positive _________ number, $\sqrt[n]{x}$ represents an even root.
Fill in the blanks.$\sqrt{0}=$ _________
Fill in the blanks.The _________ deviation of a set of numbers is the positive square root of the mean of the squares of the differences of the numbers from the mean.
Identify the radicand in each expression.$\sqrt{3 x^2}$
Identify the radicand in each expression.$5 \sqrt{x}$
Identify the radicand in each expression.$a b^2 \sqrt{a^2+b^3}$
Identify the radicand in each expression.$\frac{1}{2} x \sqrt{\frac{x}{y}}$
Find each square root, if possible.$\sqrt{121}$
Find each square root, if possible.$\sqrt{144}$
Find each square root, if possible.$-\sqrt{64}$
Find each square root, if possible.$-\sqrt{1}$
Find each square root, if possible.$\sqrt{\frac{1}{9}}$
Find each square root, if possible.$-\sqrt{\frac{4}{25}}$
Find each square root, if possible.$-\sqrt{\frac{25}{49}}$
Find each square root, if possible.$\sqrt{\frac{49}{81}}$
Find each square root, if possible.$\sqrt{-25}$
Find each square root, if possible.$\sqrt{0.25}$
Find each square root, if possible.$\sqrt{0.16}$
Find each square root, if possible.$\sqrt{-49}$
Find each square root, if possible.$\sqrt{(-4)^2}$
Find each square root, if possible.$\sqrt{(-9)^2}$
Find each square root, if possible.$\sqrt{-36}$
Find each square root, if possible.$-\sqrt{-4}$
Use a calculator to find each square root. Give the answer to four decimal places.$\sqrt{12}$
Use a calculator to find each square root. Give the answer to four decimal places.$\sqrt{340}$
Use a calculator to find each square root. Give the answer to four decimal places.$\sqrt{679.25}$
Use a calculator to find each square root. Give the answer to four decimal places.$\sqrt{0.0063}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{4 x^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{16 y^4}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{9 a^4}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{16 b^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{(t+5)^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{(a+6)^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{(-5 b)^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{(-8 c)^2}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{a^2+6 a+9}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{x^2+10 x+25}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{t^2+24 t+144}$
Find each square root. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt{m^2+30 m+225}$
Simplify each cube root.$\sqrt[3]{1}$
Simplify each cube root.$\sqrt[3]{-8}$
Simplify each cube root.$\sqrt[3]{-125}$
Simplify each cube root.$\sqrt[3]{512}$
Simplify each cube root.$\sqrt[3]{-\frac{8}{27}}$
Simplify each cube root.$\sqrt[3]{\frac{125}{216}}$
Simplify each cube root.$\sqrt[3]{0.064}$
Simplify each cube root.$\sqrt[3]{0.001}$
Simplify each cube root.$\sqrt[3]{8 a^3}$
Simplify each cube root.$\sqrt[3]{-27 x^6}$
Simplify each cube root.$\sqrt[3]{-1,000 p^3 q^3}$
Simplify each cube root.$\sqrt[3]{343 a^6 b^3}$
Simplify each cube root.$\sqrt[3]{-\frac{1}{8} m^6 n^3}$
Simplify each cube root.$\sqrt[3]{\frac{27}{1,000} a^6 b^6}$
Simplify each cube root.$\sqrt[3]{0.008 z^9}$
Simplify each cube root.$\sqrt[3]{0.064 s^9 t^6}$
Simplify each radical, if possible.$\sqrt[4]{81}$
Simplify each radical, if possible.$\sqrt[6]{64}$
Simplify each radical, if possible.$-\sqrt[5]{243}$
Simplify each radical, if possible.$-\sqrt[4]{625}$
Simplify each radical, if possible.$\sqrt[5]{-32}$
Simplify each radical, if possible.$\sqrt[6]{729}$
Simplify each radical, if possible.$\sqrt[4]{\frac{16}{625}}$
Simplify each radical, if possible.$\sqrt[5]{-\frac{243}{32}}$
Simplify each radical, if possible.$-\sqrt[5]{-\frac{1}{32}}$
Simplify each radical, if possible.$\sqrt[6]{-729}$
Simplify each radical, if possible.$-\sqrt[4]{\frac{81}{256}}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[4]{16 x^4}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[5]{32 a^5}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[3]{8 a^3}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[6]{64 x^6}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[4]{\frac{1}{16} x^4}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[4]{\frac{1}{81} x^8}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[4]{x^{12}}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[8]{x^{24}}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[5]{-x^5}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[3]{-x^6}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[3]{-27 a^6}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols where necessary.$\sqrt[5]{-32 x^5}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt[25]{(x+2)^{25}}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt[44]{(x+4)^{44}}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt[8]{0.00000001 x^{16} y^8}$
Simplify each radical. Assume that all variables are unrestricted, and use absolute value symbols when necessary.$\sqrt[5]{0.00032 x^{10} y^5}$
Find each value given that $f(x)=\sqrt{x-4}$.$f(4)$
Find each value given that $f(x)=\sqrt{x-4}$.$f(8)$
Find each value given that $f(x)=\sqrt{x-4}$.$f(20)$
Find each value given that $f(x)=\sqrt{x-4}$.$f(29)$
Find each value given that $g(x)=\sqrt{x-8}$$g(9)$
Find each value given that $g(x)=\sqrt{x-8}$$g(17)$
Find each value given that $g(x)=\sqrt{x-8}$$g(8.25)$
Find each value given that $g(x)=\sqrt{x-8}$$g(8.64)$
Find each value given that $f(x)=\sqrt{x^2+1}$. Give each answer to four decimal places.$f(4)$
Find each value given that $f(x)=\sqrt{x^2+1}$. Give each answer to four decimal places.$f(6)$
Find each value given that $f(x)=\sqrt{x^2+1}$. Give each answer to four decimal places.$f(2.35)$
Find each value given that $f(x)=\sqrt{x^2+1}$. Give each answer to four decimal places.$f(21.57)$
Graph each function and find its domain and range.$f(x)=\sqrt{x+4}$(Graph can't Copy)
Graph each function and find its domain and range.$f(x)=-\sqrt{x-2}$(Graph can't Copy)
Graph each function and find its domain and range.$f(x)=-\sqrt{x}-3$(Graph can't Copy)
Graph each function and find its domain and range.$f(x)=\sqrt[3]{x}-1$(Graph can't Copy)
Find the standard deviation of the following distribution to the nearest hundredth: $2,5,5,6,7$.
Find the standard deviation of the following distribution to the nearest hundredth: $3,6,7,9,11,12$.
In statistics, the formula$$s_{\bar{x}}=\frac{s}{\sqrt{N}}$$gives an estimate of the standard error of the mean. Find $s_{\bar{x}}$ to four decimal places when $s=65$ and $N=30$.
In statistics, the formula$$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{N}}$$gives the standard deviation of means of samples of size $N$. Find $\sigma_{\bar{x}}$ to four decimal places when $\sigma=12.7$ and $N=32$.
Radius of a circle The radius $r$ of a circle is given by the formula $r=\sqrt{\frac{4}{\pi}}$, where $A$ is its area. Find the radius of a circle whose area is $9 \pi$ square units.
Diagonal of a baseball diamond The diagonal $d$ of a square is given by the formula $d=\sqrt{2 s^2}$, where $s$ is the length of each side. Find the diagonal of the baseball diamond.(Image can't Copy)
Falling objects The time $t$ (in seconds) that it will take for an object to fall a distance of $s$ feet is given by the formula$$t=\frac{\sqrt{s}}{4}$$If a stone is dropped down a 256 -foot well, how long will it take it to hit bottom?
Police sometimes use the formula $s=k \sqrt{l}$ to estimate the speed $s$ (in mph ) of a car involved in an accident. In this formula, $l$ is the length of the skid in feet, and $k$ is a constant depending on the condition of the pavement. For wet pavement, $k \approx 3.24$. How fast was a car going if its skid was 400 feet on wet pavement?
When the resistance in a circuit is 18 ohms , the current $I$ (measured in amperes) and the power $P$ (measured in watts) are related by the formula$$I=\sqrt{\frac{P}{18}}$$Find the current used by an electrical appliance that is rated at 980 watts.
Medicine The approximate pulse rate $p$ (in beats per minute) of an adult who is $t$ inches tall is given by the formula$$p=\frac{590}{\sqrt{t}}$$Find the approximate pulse rate of an adult who is 71 inches tall.
If $x$ is any real number, then $\sqrt{x^2}=x$ is not correct. Explain.
If $x$ is any real number, then $\sqrt[3]{x^3}=|x|$ is not correct. Explain.
127. Is $\sqrt{x^2-4 x+4}=x-2$ ? What are the exceptions?
When is $\sqrt{x^2} \neq x$ ?