Question 1

Divide and simplify.
-$\frac{\sqrt{4}}{\sqrt{36}}$

Accepted Answer

A)  $3 \sqrt{4}$ 
B)  $\frac{\sqrt{4}}{3}$ 
C)  $\frac{1}{3}$ 
D)  4 
A)  $3 \sqrt{4}$ 
B)  $\frac{\sqrt{4}}{3}$ 
C)  $\frac{1}{3}$ 
D)  4 C

Question 2

Write the word or phrase that best completes each statement or answers the question.
-Why should you simplify each term in a radical expression before attempting to collect like radical terms?

Accepted Answer

It might not be possible to identify all the like radical terms until each term has been simplified

Question 3

Rationalize the denominator and simplify.
-$\frac{\sqrt{5}+2}{\sqrt{7}+6}$

Accepted Answer

A)  $\frac{\sqrt{35}+12+2 \sqrt{7}+6 \sqrt{5}}{29}$ 
B)  $\frac{\sqrt{35}-12+2 \sqrt{7}-6 \sqrt{5}}{43}$ 
C)  $\frac{\sqrt{35}+12+2 \sqrt{7}+6 \sqrt{5}}{43}$ 
D)  $\frac{-\sqrt{35}+12-2 \sqrt{7}+6 \sqrt{5}}{29}$ 
A)  $\frac{\sqrt{35}+12+2 \sqrt{7}+6 \sqrt{5}}{29}$ 
B)  $\frac{\sqrt{35}-12+2 \sqrt{7}-6 \sqrt{5}}{43}$ 
C)  $\frac{\sqrt{35}+12+2 \sqrt{7}+6 \sqrt{5}}{43}$ 
D)  $\frac{-\sqrt{35}+12-2 \sqrt{7}+6 \sqrt{5}}{29}$ D

Question 4

Add or subtract. Simplify by collecting like radical terms, if possible.
-$-2 \sqrt{48}-4 \sqrt{192}+3 \sqrt{108}$

Accepted Answer

A)  $-2 \sqrt{3}$ 
B)  $-138 \sqrt{3}$ 
C)  $-22 \sqrt{3}$ 
D)  $138 \sqrt{3}$ 
A)  $-2 \sqrt{3}$ 
B)  $-138 \sqrt{3}$ 
C)  $-22 \sqrt{3}$ 
D)  $138 \sqrt{3}$

Question 5

Add or subtract. Simplify by collecting like radical terms, if possible.
-$\sqrt{128}+9 \sqrt{32}+5 \sqrt{98}$

Accepted Answer

A)  $79 \sqrt{2}$ 
B)  $-32 \sqrt{2}$ 
C)  $-79 \sqrt{2}$ 
D)  $-4 \sqrt{2}$ 
A)  $79 \sqrt{2}$ 
B)  $-32 \sqrt{2}$ 
C)  $-79 \sqrt{2}$ 
D)  $-4 \sqrt{2}$

Question 6

Solve the equation.
-$y=\sqrt{2 y+15}$

Accepted Answer

A)  No solution 
B)  2 
C)  $5,-3$ 
D)  5 
A)  No solution 
B)  2 
C)  $5,-3$ 
D)  5

Question 7

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt{1.93}$

Accepted Answer

A)  1.404 
B)  1.389 
C)  1.376 
D)  1 
A)  1.404 
B)  1.389 
C)  1.376 
D)  1

Question 8

Multiply and then, if possible, simplify by factoring.
-$\sqrt{3} \sqrt{6}$

Accepted Answer

A)  $\sqrt{18}$ 
B)  $9 \sqrt{2}$ 
C)  $\sqrt{2}$ 
D)  $3 \sqrt{2}$ 
A)  $\sqrt{18}$ 
B)  $9 \sqrt{2}$ 
C)  $\sqrt{2}$ 
D)  $3 \sqrt{2}$

Question 9

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt{227}$

Accepted Answer

A)  15.082 
B)  15.067 
C)  15 
D)  15.054 
A)  15.082 
B)  15.067 
C)  15 
D)  15.054

Question 10

Identify the radicand.
-$\sqrt{x+3}$

Accepted Answer

A)  $x+3$ 
B)  $\sqrt{ }$ 
C)  $\sqrt{x+3}$ 
D)  $\mathrm{x}$ 
A)  $x+3$ 
B)  $\sqrt{ }$ 
C)  $\sqrt{x+3}$ 
D)  $\mathrm{x}$

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.
-$b=20, c=25$

Accepted Answer

A)  $a=225$ 
B)  $a=5$ 
C)  $a=45$ 
D)  $a=15$ 
A)  $a=225$ 
B)  $a=5$ 
C)  $a=45$ 
D)  $a=15$

Question 12

Multiply and then, if possible, simplify by factoring.
-$\sqrt{3 x} \sqrt{81 y}$

Accepted Answer

A)  $81 \sqrt{x y}$ 
B)  $9 x y$ 
C)  $9 \sqrt{3 x y}$ 
D)  $\sqrt{81 x y}$ 
A)  $81 \sqrt{x y}$ 
B)  $9 x y$ 
C)  $9 \sqrt{3 x y}$ 
D)  $\sqrt{81 x y}$

Question 13

Solve the problem.
-The cost of manufacturing clocks is given by $c=100 \sqrt{n+36}$, where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

Accepted Answer

A)  $\$ 600$ 
B)  $\$ 60$ 
C)  $\$ 3600$ 
D)  $\$ 100$ 
A)  $\$ 600$ 
B)  $\$ 60$ 
C)  $\$ 3600$ 
D)  $\$ 100$

Question 14

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

Accepted Answer

A)  $\sqrt{\mathrm{z}}-2$ 
B)  $z-2$ 
C)  $(z-2)^{2}$ 
D)  $z-\sqrt{2}$ 
A)  $\sqrt{\mathrm{z}}-2$ 
B)  $z-2$ 
C)  $(z-2)^{2}$ 
D)  $z-\sqrt{2}$

Question 15

Divide and simplify.
-$\frac{\sqrt{32 x}}{\sqrt{2 x}}$

Accepted Answer

A)  4 
B)  $4 x$ 
C)  $2 x$ 
D)  2 
A)  4 
B)  $4 x$ 
C)  $2 x$ 
D)  2

Question 16

Write the word or phrase that best completes each statement or answers the question.
-Why must you know how to add and subtract radical expressions before you can rationalize denominators with two terms?

Accepted Answer

After multiplying to rationali

Question 17

Multiply and then, if possible, simplify by factoring.
-$\sqrt{125} \sqrt{5}$

Accepted Answer

A)  625 
B)  25 
C)  $5 \sqrt{5}$ 
D)  $5 \sqrt{25}$ 
A)  625 
B)  25 
C)  $5 \sqrt{5}$ 
D)  $5 \sqrt{25}$

Question 18

Perform the indicated operation.
-$(\sqrt{8}+\sqrt{7})(\sqrt{8}-\sqrt{7})$

Accepted Answer

A)  1 
B)  15 
C)  $8-4 \sqrt{28}$ 
D)  $8-2 \sqrt{56}$ 
A)  1 
B)  15 
C)  $8-4 \sqrt{28}$ 
D)  $8-2 \sqrt{56}$

Question 19

Perform the indicated operation.
-$\sqrt{7}(3 \sqrt{7}-\sqrt{7})$

Accepted Answer

A)  $21-\sqrt{7}$ 
B)  14 
C)  $7 \sqrt{3}-7$ 
D)  28 
A)  $21-\sqrt{7}$ 
B)  14 
C)  $7 \sqrt{3}-7$ 
D)  28

Question 20

Add or subtract. Simplify by collecting like radical terms, if possible.
-$\sqrt{3 a}+4 \sqrt{75 a}-7 \sqrt{12 a}$

Accepted Answer

A)  $7 \sqrt{3 a}$ 
B)  $7 \sqrt{90 a}$ 
C)  $-3 \sqrt{3 a}$ 
D)  $-3 \sqrt{90 a}$ 
A)  $7 \sqrt{3 a}$ 
B)  $7 \sqrt{90 a}$ 
C)  $-3 \sqrt{3 a}$ 
D)  $-3 \sqrt{90 a}$

Divide and simplify. - $\frac{\sqrt{4}}{\sqrt{36}}$

Write the word or phrase that best completes each statement or answers the question. -Why should you simplify each term in a radical expression before attempting to collect like radical terms?

Rationalize the denominator and simplify. - $\frac{\sqrt{5}+2}{\sqrt{7}+6}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $-2 \sqrt{48}-4 \sqrt{192}+3 \sqrt{108}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{128}+9 \sqrt{32}+5 \sqrt{98}$

Solve the equation. - $y=\sqrt{2 y+15}$

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{1.93}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{3} \sqrt{6}$

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{227}$

Identify the radicand. - $\sqrt{x+3}$

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. - $b=20, c=25$

Multiply and then, if possible, simplify by factoring. - $\sqrt{3 x} \sqrt{81 y}$

Solve the problem. -The cost of manufacturing clocks is given by $c=100 \sqrt{n+36}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

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

Divide and simplify. - $\frac{\sqrt{32 x}}{\sqrt{2 x}}$

Write the word or phrase that best completes each statement or answers the question. -Why must you know how to add and subtract radical expressions before you can rationalize denominators with two terms?

Multiply and then, if possible, simplify by factoring. - $\sqrt{125} \sqrt{5}$

Perform the indicated operation. - $(\sqrt{8}+\sqrt{7})(\sqrt{8}-\sqrt{7})$

Perform the indicated operation. - $\sqrt{7}(3 \sqrt{7}-\sqrt{7})$

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{3 a}+4 \sqrt{75 a}-7 \sqrt{12 a}$

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

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

Converting Units of Measurement

Filters

Exam 14: Radical Expressions and Equations

Divide and simplify. - 436\frac{\sqrt{4}}{\sqrt{36}}36​4​​

Write the word or phrase that best completes each statement or answers the question. -Why should you simplify each term in a radical expression before attempting to collect like radical terms?

Rationalize the denominator and simplify. - 5+27+6\frac{\sqrt{5}+2}{\sqrt{7}+6}7​+65​+2​

Add or subtract. Simplify by collecting like radical terms, if possible. - −248−4192+3108-2 \sqrt{48}-4 \sqrt{192}+3 \sqrt{108}−248​−4192​+3108​

Add or subtract. Simplify by collecting like radical terms, if possible. - 128+932+598\sqrt{128}+9 \sqrt{32}+5 \sqrt{98}128​+932​+598​

Solve the equation. - y=2y+15y=\sqrt{2 y+15}y=2y+15​

Use a calculator to approximate the square root. Round to three decimal places. - 1.93\sqrt{1.93}1.93​

Multiply and then, if possible, simplify by factoring. - 36\sqrt{3} \sqrt{6}3​6​

Use a calculator to approximate the square root. Round to three decimal places. - 227\sqrt{227}227​

Identify the radicand. - x+3\sqrt{x+3}x+3​

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. - b=20,c=25b=20, c=25b=20,c=25

Multiply and then, if possible, simplify by factoring. - 3x81y\sqrt{3 x} \sqrt{81 y}3x​81y​

Solve the problem. -The cost of manufacturing clocks is given by c=100n+36c=100 \sqrt{n+36}c=100n+36​ , where ccc is the total cost and nnn is the number produced. What is c\mathrm{c}c when no clocks are produced?

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - (z−2)2\sqrt{(\mathrm{z}-2)^{2}}(z−2)2​

Divide and simplify. - 32x2x\frac{\sqrt{32 x}}{\sqrt{2 x}}2x​32x​​