Question 1

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places.
-

Accepted Answer

A)  $\sqrt{569} \approx 23.854$ 
B)  231 
C)  $\sqrt{7} \approx 2.646$ 
D)  $\sqrt{231} \approx 15.199$ 
A)  $\sqrt{569} \approx 23.854$ 
B)  231 
C)  $\sqrt{7} \approx 2.646$ 
D)  $\sqrt{231} \approx 15.199$

Question 2

Perform the indicated operation.
-$\sqrt{3}(5 \sqrt{3}-\sqrt{3})$

Accepted Answer

A)  $15-\sqrt{3}$ 
B)  $3 \sqrt{5}-3$ 
C)  18 
D)  12 
A)  $15-\sqrt{3}$ 
B)  $3 \sqrt{5}-3$ 
C)  18 
D)  12

Question 3

Multiply and then, if possible, simplify by factoring.
-$\sqrt{7} \sqrt{3 \mathrm{x}+1}$

Accepted Answer

A)  $21 \mathrm{x}-7$ 
B)  $\sqrt{21 \mathrm{x}-7}$ 
C)  $\sqrt{21 x+7}$ 
D)  $\sqrt{21 x+1}$ 
A)  $21 \mathrm{x}-7$ 
B)  $\sqrt{21 \mathrm{x}-7}$ 
C)  $\sqrt{21 x+7}$ 
D)  $\sqrt{21 x+1}$

Question 4

Identify the radicand.
-$4 \mathrm{ab} \sqrt{\mathrm{b}^{2}-9}$

Accepted Answer

A)  $b^{2}$ 
B)  $\sqrt{b^{2}-9}$ 
C)  $b^{2}-9$ 
D)  $4 \mathrm{ab}$ 
A)  $b^{2}$ 
B)  $\sqrt{b^{2}-9}$ 
C)  $b^{2}-9$ 
D)  $4 \mathrm{ab}$

Question 5

Solve the problem.
-The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.3 \sqrt{h}$, where $h$ is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 17.5 miles?

Accepted Answer

A)  $135 \mathrm{ft}$ 
B)  $398 \mathrm{ft}$ 
C)  $181 \mathrm{ft}$ 
D)  $306 \mathrm{ft}$ 
A)  $135 \mathrm{ft}$ 
B)  $398 \mathrm{ft}$ 
C)  $181 \mathrm{ft}$ 
D)  $306 \mathrm{ft}$

Question 6

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt{0.000191}$

Accepted Answer

A)  0.014 
B)  0.14 
C)  1.400 
D)  0.001 
A)  0.014 
B)  0.14 
C)  1.400 
D)  0.001

Question 7

Rationalize the denominator and simplify.
-$\frac{4 \sqrt{13}}{6 \sqrt{3}}$

Accepted Answer

A)  $\frac{2 \sqrt{39}}{3}$ 
B)  $\frac{2 \sqrt{13}}{3}$ 
C)  $\frac{2 \sqrt{13}}{9}$ 
D)  $\frac{2 \sqrt{39}}{9}$ 
A)  $\frac{2 \sqrt{39}}{3}$ 
B)  $\frac{2 \sqrt{13}}{3}$ 
C)  $\frac{2 \sqrt{13}}{9}$ 
D)  $\frac{2 \sqrt{39}}{9}$

Question 8

Multiply and then, if possible, simplify by factoring.
-$\sqrt{3} \sqrt{15}$

Accepted Answer

A)  $9 \sqrt{5}$ 
B)  $\sqrt{45}$ 
C)  $\sqrt{5}$ 
D)  $3 \sqrt{5}$ 
A)  $9 \sqrt{5}$ 
B)  $\sqrt{45}$ 
C)  $\sqrt{5}$ 
D)  $3 \sqrt{5}$

Question 9

Perform the indicated operation.
-$(5+\sqrt{12})(5-\sqrt{12})$

Accepted Answer

A)  -7 
B)  37 
C)  13 
D)  $5-2 \sqrt{12}$ 
A)  -7 
B)  37 
C)  13 
D)  $5-2 \sqrt{12}$

Question 10

Solve the equation.
-$\sqrt{x^{2}-9 x+21}=x-5$

Accepted Answer

A)  46 
B)  4 
C)  $\frac{46}{9}$ 
D)  No solution 
A)  46 
B)  4 
C)  $\frac{46}{9}$ 
D)  No solution

Question 11

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places.
-$a=1, b=9$

Accepted Answer

A)  $\mathrm{c}=\sqrt{10} ; \mathrm{c} \approx 3.162$ 
B)  $\mathrm{c}=\sqrt{80} ; \mathrm{c} \approx 8.944$ 
C)  $\mathrm{c}=\sqrt{82} ; \mathrm{c} \approx 9.055$ 
D)  $\mathrm{C}=10$ 
A)  $\mathrm{c}=\sqrt{10} ; \mathrm{c} \approx 3.162$ 
B)  $\mathrm{c}=\sqrt{80} ; \mathrm{c} \approx 8.944$ 
C)  $\mathrm{c}=\sqrt{82} ; \mathrm{c} \approx 9.055$ 
D)  $\mathrm{C}=10$

Question 12

Multiply and then, if possible, simplify by factoring.
-$\sqrt{2 x^{2} y} \sqrt{6 x^{5} y^{6}}$

Accepted Answer

A)  $2 x^{3} y^{3} \sqrt{3}$ 
B)  $2 \sqrt{3 x^{7} y^{7}}$ 
C)  $2 x^{3} y^{3} \sqrt{3 x y}$ 
D)  $4 x^{6} y^{6} \sqrt{3 x y}$ 
A)  $2 x^{3} y^{3} \sqrt{3}$ 
B)  $2 \sqrt{3 x^{7} y^{7}}$ 
C)  $2 x^{3} y^{3} \sqrt{3 x y}$ 
D)  $4 x^{6} y^{6} \sqrt{3 x y}$

Question 13

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{49 x^{2}}$

Accepted Answer

A)  $49 x$ 
B)  $7 x^{2}$ 
C)  $7 \mathrm{x}$ 
D)  $-7 \mathrm{x}$ 
A)  $49 x$ 
B)  $7 x^{2}$ 
C)  $7 \mathrm{x}$ 
D)  $-7 \mathrm{x}$

Question 14

Perform the indicated operation.
-$(\sqrt{10}+5)(\sqrt{10}-5)$

Accepted Answer

A)  -15 
B)  $10-2 \sqrt{5}$ 
C)  5 
D)  35 
A)  -15 
B)  $10-2 \sqrt{5}$ 
C)  5 
D)  35

Question 15

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{\left(9 x^{2}\right)^{2}}$

Accepted Answer

A)  $3 x^{2}$ 
B)  $9 \mathrm{x}$ 
C)  $3 \mathrm{x}$ 
D)  $9 x^{2}$ 
A)  $3 x^{2}$ 
B)  $9 \mathrm{x}$ 
C)  $3 \mathrm{x}$ 
D)  $9 x^{2}$

Question 16

Solve the problem.
-The distance in miles that can be seen on the surface of the ocean is given by $d=1.4 \sqrt{h}$ where $h$ is the height above the surface of the water. How many feet high above the water (to the nearest tenth) would a pirate have to climb to see 17 miles?

Accepted Answer

A)  $73.7 \mathrm{ft}$ 
B)  $147.4 \mathrm{ft}$ 
C)  $566.4 \mathrm{ft}$ 
D)  $5.8 \mathrm{ft}$ 
A)  $73.7 \mathrm{ft}$ 
B)  $147.4 \mathrm{ft}$ 
C)  $566.4 \mathrm{ft}$ 
D)  $5.8 \mathrm{ft}$

Question 17

Divide and simplify.
-$\frac{\sqrt{180 x^{3}}}{\sqrt{5 x}}$

Accepted Answer

A)  $5 \mathrm{x}$ 
B)  $6 x$ 
C)  $6 x^{2}$ 
D)  5 
A)  $5 \mathrm{x}$ 
B)  $6 x$ 
C)  $6 x^{2}$ 
D)  5

Question 18

Rationalize the denominator and simplify.
-$\frac{5 x}{\sqrt{3}}$

Accepted Answer

A)  $\frac{5 x \sqrt{3}}{3}$ 
B)  14 
C)  $\frac{25 x \sqrt{3}}{3}$ 
D)  $5 x \sqrt{3}$ 
A)  $\frac{5 x \sqrt{3}}{3}$ 
B)  14 
C)  $\frac{25 x \sqrt{3}}{3}$ 
D)  $5 x \sqrt{3}$

Question 19

Simplify by factoring.
-$\sqrt{25 z+10 z^{2}+z^{3}}$

Accepted Answer

A)  $\sqrt{z}+\sqrt{|5|}$ 
B)  $\sqrt{\mathrm{z}}(\mathrm{z}+5)$ 
C)  $(z+5)^{2}$ 
D)  $z+5$ 
A)  $\sqrt{z}+\sqrt{|5|}$ 
B)  $\sqrt{\mathrm{z}}(\mathrm{z}+5)$ 
C)  $(z+5)^{2}$ 
D)  $z+5$

Question 20

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places.
-$\mathrm{a}=\sqrt{3}, \mathrm{c}=\sqrt{10}$

Accepted Answer

A)  $b=\sqrt{7}, b \approx 2.646$ 
B)  $b=2 \sqrt{2}, b \approx 2.828$ 
C)  $b=7$ 
D)  $b=2 \sqrt{7}, b \approx 5.292$ 
A)  $b=\sqrt{7}, b \approx 2.646$ 
B)  $b=2 \sqrt{2}, b \approx 2.828$ 
C)  $b=7$ 
D)  $b=2 \sqrt{7}, b \approx 5.292$

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Perform the indicated operation. - $\sqrt{3}(5 \sqrt{3}-\sqrt{3})$

Multiply and then, if possible, simplify by factoring. - $\sqrt{7} \sqrt{3 \mathrm{x}+1}$

Identify the radicand. - $4 \mathrm{ab} \sqrt{\mathrm{b}^{2}-9}$

Solve the problem. -The distance $d$ in miles that can be seen on the surface of the ocean is given by $d=1.3 \sqrt{h}$ , where $h$ is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 17.5 miles?

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{0.000191}$

Rationalize the denominator and simplify. - $\frac{4 \sqrt{13}}{6 \sqrt{3}}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{3} \sqrt{15}$

Perform the indicated operation. - $(5+\sqrt{12})(5-\sqrt{12})$

Solve the equation. - $\sqrt{x^{2}-9 x+21}=x-5$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $a=1, b=9$

Multiply and then, if possible, simplify by factoring. - $\sqrt{2 x^{2} y} \sqrt{6 x^{5} y^{6}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{49 x^{2}}$

Perform the indicated operation. - $(\sqrt{10}+5)(\sqrt{10}-5)$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{\left(9 x^{2}\right)^{2}}$

Solve the problem. -The distance in miles that can be seen on the surface of the ocean is given by $d=1.4 \sqrt{h}$ where $h$ is the height above the surface of the water. How many feet high above the water (to the nearest tenth) would a pirate have to climb to see 17 miles?

Divide and simplify. - $\frac{\sqrt{180 x^{3}}}{\sqrt{5 x}}$

Rationalize the denominator and simplify. - $\frac{5 x}{\sqrt{3}}$

Simplify by factoring. - $\sqrt{25 z+10 z^{2}+z^{3}}$

Find the length of the third side of the right triangle. Assume that $c$ represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - $\mathrm{a}=\sqrt{3}, \mathrm{c}=\sqrt{10}$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

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Exam 8: Radical Expressions and Equations

Find the length of the third side of the right triangle. Where appropriate, give both an exact answer and an approximation to three decimal places. -

Perform the indicated operation. - 3(53−3)\sqrt{3}(5 \sqrt{3}-\sqrt{3})3​(53​−3​)

Multiply and then, if possible, simplify by factoring. - 73x+1\sqrt{7} \sqrt{3 \mathrm{x}+1}7​3x+1​

Identify the radicand. - 4abb2−94 \mathrm{ab} \sqrt{\mathrm{b}^{2}-9}4abb2−9​

Solve the problem. -The distance ddd in miles that can be seen on the surface of the ocean is given by d=1.3hd=1.3 \sqrt{h}d=1.3h​ , where hhh is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 17.5 miles?

Use a calculator to approximate the square root. Round to three decimal places. - 0.000191\sqrt{0.000191}0.000191​

Rationalize the denominator and simplify. - 41363\frac{4 \sqrt{13}}{6 \sqrt{3}}63​413​​

Multiply and then, if possible, simplify by factoring. - 315\sqrt{3} \sqrt{15}3​15​

Perform the indicated operation. - (5+12)(5−12)(5+\sqrt{12})(5-\sqrt{12})(5+12​)(5−12​)

Solve the equation. - x2−9x+21=x−5\sqrt{x^{2}-9 x+21}=x-5x2−9x+21​=x−5

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - a=1,b=9a=1, b=9a=1,b=9

Multiply and then, if possible, simplify by factoring. - 2x2y6x5y6\sqrt{2 x^{2} y} \sqrt{6 x^{5} y^{6}}2x2y​6x5y6​

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - 49x2\sqrt{49 x^{2}}49x2​

Perform the indicated operation. - (10+5)(10−5)(\sqrt{10}+5)(\sqrt{10}-5)(10​+5)(10​−5)

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - (9x2)2\sqrt{\left(9 x^{2}\right)^{2}}(9x2)2​

Solve the problem. -The distance in miles that can be seen on the surface of the ocean is given by d=1.4hd=1.4 \sqrt{h}d=1.4h​ where hhh is the height above the surface of the water. How many feet high above the water (to the nearest tenth) would a pirate have to climb to see 17 miles?

Divide and simplify. - 180x35x\frac{\sqrt{180 x^{3}}}{\sqrt{5 x}}5x​180x3​​

Rationalize the denominator and simplify. - 5x3\frac{5 x}{\sqrt{3}}3​5x​

Simplify by factoring. - 25z+10z2+z3\sqrt{25 z+10 z^{2}+z^{3}}25z+10z2+z3​

Find the length of the third side of the right triangle. Assume that ccc represents the length of the hypotenuse. Give an exact answer and, if appropriate, an approximation to three decimal places. - a=3,c=10\mathrm{a}=\sqrt{3}, \mathrm{c}=\sqrt{10}a=3​,c=10​