Section 1
Square Roots
Complete: since $(-2)^{2}=4,-2$ is a ____ of 4.
State the meaning of the symbols $\sqrt,-\sqrt{,}$ and $\pm \sqrt{\text { }}$ when applied to apositive number $n$
Identify the radicand in the equation $\sqrt{4}=2$
Evaluate the expression.$$\sqrt{81}$$
Evaluate the expression.$$\pm \sqrt{121}$$
Evaluate the expression.$$-\sqrt{36}$$
Evaluate the expression.$$-\sqrt{4}$$
Determine whether each expression is rational or irrational.$$\sqrt{25}$$
Determine whether each expression is rational or irrational.$$\sqrt{6}$$
Determine whether each expression is rational or irrational.$$\sqrt{100}$$
Determine whether each expression is rational or irrational.$$\sqrt{10}$$
Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth.$$1 \pm \sqrt{2}$$
Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth.$$6 \pm 5 \sqrt{3}$$
Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth.$$3 \pm \sqrt{7}$$
Use a calculator or a table of square roots to evaluate the expression. Round the results to the nearest hundredth.$$2 \pm 4 \sqrt{8}$$
Write the equation in words.$$\sqrt{625}=25$$
Write the equation in words.$$\pm \sqrt{16}=\pm 4$$
Write the equation in words.$$\pm \sqrt{4}=\pm 2$$
Write the equation in words.$$\sqrt{225}=15$$
Write the equation in words.$$-\sqrt{121}=-11$$
Write the equation in words.$$-\sqrt{289}=-17$$
Write the equation in words.$$\sqrt{49}=7$$
Write the equation in words.$$\sqrt{1}=1$$
Write the equation in words.$$\sqrt{\frac{1}{9}}=\frac{1}{3}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{144}$$
Evaluate the expression. Check the results by squaring each root.$$\pm \sqrt{25}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{196}$$
Evaluate the expression. Check the results by squaring each root.$$\pm \sqrt{900}$$
Evaluate the expression. Check the results by squaring each root.$$\pm \sqrt{49}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{0}$$
Evaluate the expression. Check the results by squaring each root.$$-\sqrt{256}$$
Evaluate the expression. Check the results by squaring each root.$$-\sqrt{100}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{400}$$
Evaluate the expression. Check the results by squaring each root.$$-\sqrt{225}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{121}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{289}$$
Evaluate the expression. Check the results by squaring each root.$$-\sqrt{1}$$
Evaluate the expression. Check the results by squaring each root.$$\pm \sqrt{81}$$
Evaluate the expression. Check the results by squaring each root.$$\sqrt{169}$$
Evaluate the expression. Check the results by squaring each root.$$-\sqrt{625}$$
Determine whether the number is a perfect square.$$10$$
Determine whether the number is a perfect square.$$81$$
Determine whether the number is a perfect square.$$-5$$
Determine whether the number is a perfect square.$$120$$
Determine whether the number is a perfect square.$$16$$
Determine whether the number is a perfect square.$$1$$
Determine whether the number is a perfect square.$$111$$
Determine whether the number is a perfect square.$$225$$
Determine whether the number is a perfect square.$$-4$$
Determine whether the number is a perfect square.$$10,000$$
Determine whether the number is a perfect square.$$\frac{9}{4}$$
Determine whether the number is a perfect square.$$\frac{1}{2}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\sqrt{5}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\sqrt{25}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\sqrt{13}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$-\sqrt{125}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$-\sqrt{49}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\pm \sqrt{70}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\pm \sqrt{1}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\sqrt{10}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\pm \sqrt{15}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$-\sqrt{400}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$-\sqrt{20}$$
Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth.$$\pm \sqrt{144}$$
Evaluate $\sqrt{b^{2}-4 a c}$ for the given values.$$a=4, b=5, c=1$$
Evaluate $\sqrt{b^{2}-4 a c}$ for the given values.$$a=2, b=4, c=-6$$
Evaluate $\sqrt{b^{2}-4 a c}$ for the given values.$$a=-2, b=8, c=-8$$
Evaluate $\sqrt{b^{2}-4 a c}$ for the given values.$$a=-5, b=5, c=10$$
Evaluate the radical expression when a = 2 and b = 4.$$\sqrt{b^{2}+10 a}$$
Evaluate the radical expression when a = 2 and b = 4.$$\sqrt{b^{2}-8 a}$$
Evaluate the radical expression when a = 2 and b = 4.$$\sqrt{a^{2}+45}$$
Evaluate the radical expression when a = 2 and b = 4.$$\frac{\sqrt{b^{2}+42 a}}{a}$$
Evaluate the radical expression when a = 2 and b = 4.$$\frac{10+2 \sqrt{b}}{a}$$
Evaluate the radical expression when a = 2 and b = 4.$$\frac{36-\sqrt{8 a}}{b}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$8 \pm \sqrt{5}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$2 \pm 5 \sqrt{3}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$-6 \pm 4 \sqrt{2}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{1 \pm 6 \sqrt{8}}{6}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{7 \pm 3 \sqrt{2}}{-1}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{4 \pm 7 \sqrt{3}}{2}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{5 \pm 6 \sqrt{3}}{3}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{3 \pm 4 \sqrt{5}}{4}$$
Use a calculator to evaluate the expression. Round the results to the nearest hundredth.$$\frac{7 \pm 3 \sqrt{12}}{-6}$$
A chessboard has 8 small squares on a side and therefore has a total of 64 small squares.Could a similar square game board be constructed that has a total of 81 small squares?
A chessboard has 8 small squares on a side and therefore has a total of 64 small squares.If a square game board has a total of m small squares of equal size, what can you say about m?
determine whether the statement is true or false. If it is true, give an example. If it is false, give a counterexample.All positive numbers have two different square roots.
determine whether the statement is true or false. If it is true, give an example. If it is false, give a counterexample.No number has only one square root.
determine whether the statement is true or false. If it is true, give an example. If it is false, give a counterexample.Some numbers have no real square root.
Evaluate $3 \pm \sqrt{(-3)^{2}-4(0.5)(-8)}$
Evaluate $\frac{15 \pm 5 \sqrt{225}}{3}$a. -70 and 80b. -20 and 30c. 20 and 30d. 70 and 80
Which is an example of a perfect square?a. -100 b. 10c. 121 d. 150
Which two consecutive integers does $\sqrt{200}$ fall between??a. 10 and 11b. 13 and 14c. 14 and 15d. 19 and 20
If $a^{2}=36$ and $b^{2}=49,$ choose the greatest possible value for the expression $b-a$f. -13g. -1h. 1j. 13
Graph the linear system and estimate a solution. Then check your solution algebraically.$$\begin{aligned}&y=-3\\&x=4\end{aligned}$$
Graph the linear system and estimate a solution. Then check your solution algebraically.$$\begin{aligned}2 x-4 y &=12 \\y &=-2\end{aligned}$$
Graph the linear system and estimate a solution. Then check your solution algebraically.$$\begin{array}{r}{2 x-y=10} \\{x+y=5}\end{array}$$
The admission price for a high school basketball game is $\$2$ for students and $\$3$ for adults. At one game, 324 tickets were sold and $\$764$ was collected. How many students and adults attended the game?
You are buying a combination of irises and lilies for a flower arrangement. The irises are $\$4$ each and the lilies are $\$3$ each. You spend $\$50$ for an arrangement of 15 flowers. How many of each type of flower did you buy?
Use linear combinations to solve the system of linear equations.$$\begin{aligned}&10 x-3 y=17\\&-7 x+y=9\end{aligned}$$
Use linear combinations to solve the system of linear equations.$$\begin{aligned}12 x-4 y &=-32 \\x+3 y &=4\end{aligned}$$
Use linear combinations to solve the system of linear equations.$$\begin{array}{c}{8 x-5 y=70} \\{2 x+y=4}\end{array}$$
Write the fraction as a terminating or repeating decimal.$$\frac{3}{4}$$
Write the fraction as a terminating or repeating decimal.$$\frac{8}{15}$$
Write the fraction as a terminating or repeating decimal.$$\frac{6}{11}$$
Write the fraction as a terminating or repeating decimal.$$\frac{7}{8}$$
Write the fraction as a terminating or repeating decimal.$$\frac{2}{9}$$
Write the fraction as a terminating or repeating decimal.$$\frac{5}{16}$$
Write the fraction as a terminating or repeating decimal.$$\frac{5}{6}$$
Write the fraction as a terminating or repeating decimal.$$\frac{2}{5}$$
Write the fraction as a terminating or repeating decimal.$$\frac{5}{8}$$
Write the fraction as a terminating or repeating decimal.$$\frac{8}{9}$$
Write the fraction as a terminating or repeating decimal.$$\frac{3}{5}$$
Write the fraction as a terminating or repeating decimal.$$\frac{9}{10}$$