Question 1

Add or subtract. Simplify by collecting like radical terms, if possible.
-$20 \sqrt{5}-13 \sqrt{5}$

Accepted Answer

A)  $33 \sqrt{5}$ 
B)  7 
C)  35 
D)  $7 \sqrt{5}$ 
A)  $33 \sqrt{5}$ 
B)  7 
C)  35 
D)  $7 \sqrt{5}$

Question 2

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

Accepted Answer

A)  $\frac{5 x-15 \sqrt{x y}}{x-9 y}$ 
B)  $\frac{5 x-15 \sqrt{x y}}{x+3 y}$ 
C)  $\frac{5 x-15 \sqrt{x y}}{x-3 y}$ 
D)  $\frac{5 x-15 \sqrt{x y}}{x+9 y}$ 
A)  $\frac{5 x-15 \sqrt{x y}}{x-9 y}$ 
B)  $\frac{5 x-15 \sqrt{x y}}{x+3 y}$ 
C)  $\frac{5 x-15 \sqrt{x y}}{x-3 y}$ 
D)  $\frac{5 x-15 \sqrt{x y}}{x+9 y}$

Question 3

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt{\frac{112}{95}}$

Accepted Answer

A)  1.086 
B)  0.986 
C)  1.186 
D)  2.086 
A)  1.086 
B)  0.986 
C)  1.186 
D)  2.086

Question 4

Add or subtract. Simplify by collecting like radical terms, if possible.
-$-5 x \sqrt{y^{5} x}+x \sqrt{y x^{5}}+2 y \sqrt{y^{5} x}$

Accepted Answer

A)  $\left(-5 x^{2} y^{2}+x^{3}+2 x y^{3}\right) \sqrt{x y}$ 
B)  $\left(-5 x y^{2}+x^{3}+2 y^{3}\right) \sqrt{x y}$ 
C)  $\left(-5 x y^{3}+x^{4}+2 y^{4}\right) \sqrt{x y}$ 
D)  $\left(-5 x+x^{3}+2 y^{3}\right) \sqrt{x y}$ 
A)  $\left(-5 x^{2} y^{2}+x^{3}+2 x y^{3}\right) \sqrt{x y}$ 
B)  $\left(-5 x y^{2}+x^{3}+2 y^{3}\right) \sqrt{x y}$ 
C)  $\left(-5 x y^{3}+x^{4}+2 y^{4}\right) \sqrt{x y}$ 
D)  $\left(-5 x+x^{3}+2 y^{3}\right) \sqrt{x y}$

Question 5

Multiply and then, if possible, simplify by factoring.
-$\sqrt{2 x^{2}} \sqrt{22 x^{4}}$

Accepted Answer

A)  $2 \sqrt{11 x^{6}}$ 
B)  $2 x^{3} \sqrt{11}$ 
C)  $4 x^{3} \sqrt{11}$ 
D)  $2 x^{6} \sqrt{11}$ 
A)  $2 \sqrt{11 x^{6}}$ 
B)  $2 x^{3} \sqrt{11}$ 
C)  $4 x^{3} \sqrt{11}$ 
D)  $2 x^{6} \sqrt{11}$

Question 6

Simplify by factoring.
-$\sqrt{490}$

Accepted Answer

A)  $7 \sqrt{10}$ 
B)  70 
C)  $10 \sqrt{7}$ 
D)  22 
A)  $7 \sqrt{10}$ 
B)  70 
C)  $10 \sqrt{7}$ 
D)  22

Question 7

Rationalize the denominator and simplify.
-$\frac{9}{\sqrt{14}}$

Accepted Answer

A)  $9 \sqrt{14}$ 
B)  $\frac{9 \sqrt{14}}{14}$ 
C)  205 
D)  $\frac{81 \sqrt{14}}{14}$ 
A)  $9 \sqrt{14}$ 
B)  $\frac{9 \sqrt{14}}{14}$ 
C)  205 
D)  $\frac{81 \sqrt{14}}{14}$

Question 8

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

Accepted Answer

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

Question 9

Solve the problem.
-The time $T$ in seconds for a pendulum of length $L$ feet to make one swing is given by $T=2 \pi \sqrt{\frac{L}{35}}$. How long is a pendulum (to nearest hundredth) if it makes one swing in 1.5 seconds? Use 3.14 for $\pi$.

Accepted Answer

A)  $12.54 \mathrm{ft}$ 
B)  $78.75 \mathrm{ft}$ 
C)  $2 \mathrm{ft}$ 
D)  $19.69 \mathrm{ft}$ 
A)  $12.54 \mathrm{ft}$ 
B)  $78.75 \mathrm{ft}$ 
C)  $2 \mathrm{ft}$ 
D)  $19.69 \mathrm{ft}$

Question 10

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)  394 
B)  $\sqrt{394} \approx 19.849$ 
C)  $\sqrt{184} \approx 13.565$ 
D)  $\sqrt{394}=197.0$ 
A)  394 
B)  $\sqrt{394} \approx 19.849$ 
C)  $\sqrt{184} \approx 13.565$ 
D)  $\sqrt{394}=197.0$

Question 11

Solve the equation.
-$\sqrt{\mathrm{p}^{2}-5 \mathrm{p}+81}=\mathrm{p}+4$

Accepted Answer

A)  $\frac{-5}{2}$ 
B)  9 
C)  5 
D)  -5 
A)  $\frac{-5}{2}$ 
B)  9 
C)  5 
D)  -5

Question 12

Use a calculator to approximate the square root. Round to three decimal places.
-$\sqrt{107}$

Accepted Answer

A)  10 
B)  10.359 
C)  10.344 
D)  10.331 
A)  10 
B)  10.359 
C)  10.344 
D)  10.331

Question 13

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

Accepted Answer

A)  $\frac{3 \sqrt{35}+5 \sqrt{7}}{35}$ 
B)  $\frac{-\sqrt{35}+7 \sqrt{7}}{44}$ 
C)  $\frac{-\sqrt{35}-7 \sqrt{7}}{44}$ 
D)  $\frac{\sqrt{35}-7 \sqrt{7}}{12}$ 
A)  $\frac{3 \sqrt{35}+5 \sqrt{7}}{35}$ 
B)  $\frac{-\sqrt{35}+7 \sqrt{7}}{44}$ 
C)  $\frac{-\sqrt{35}-7 \sqrt{7}}{44}$ 
D)  $\frac{\sqrt{35}-7 \sqrt{7}}{12}$

Question 14

Add or subtract. Simplify by collecting like radical terms, if possible.
-$\sqrt{3 \mathrm{a}}+4 \sqrt{27 \mathrm{a}}+3 \sqrt{12 \mathrm{a}}$

Accepted Answer

A)  $19 \sqrt{3 a}$ 
B)  $7 \sqrt{3 a}$ 
C)  $19 \sqrt{42 \mathrm{a}}$ 
D)  $7 \sqrt{42 \mathrm{a}}$ 
A)  $19 \sqrt{3 a}$ 
B)  $7 \sqrt{3 a}$ 
C)  $19 \sqrt{42 \mathrm{a}}$ 
D)  $7 \sqrt{42 \mathrm{a}}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $20 \sqrt{5}-13 \sqrt{5}$

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

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{\frac{112}{95}}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $-5 x \sqrt{y^{5} x}+x \sqrt{y x^{5}}+2 y \sqrt{y^{5} x}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{2 x^{2}} \sqrt{22 x^{4}}$

Simplify by factoring. - $\sqrt{490}$

Rationalize the denominator and simplify. - $\frac{9}{\sqrt{14}}$

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

Solve the problem. -The time $T$ in seconds for a pendulum of length $L$ feet to make one swing is given by $T=2 \pi \sqrt{\frac{L}{35}}$ . How long is a pendulum (to nearest hundredth) if it makes one swing in 1.5 seconds? Use 3.14 for $\pi$ .

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. -

Solve the equation. - $\sqrt{\mathrm{p}^{2}-5 \mathrm{p}+81}=\mathrm{p}+4$

Use a calculator to approximate the square root. Round to three decimal places. - $\sqrt{107}$

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

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{3 \mathrm{a}}+4 \sqrt{27 \mathrm{a}}+3 \sqrt{12 \mathrm{a}}$

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

Filters

Exam 8: Radical Expressions and Equations

Add or subtract. Simplify by collecting like radical terms, if possible. - 205−13520 \sqrt{5}-13 \sqrt{5}205​−135​

Rationalize the denominator and simplify. - 5xx+3y\frac{5 \sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+3 \sqrt{\mathrm{y}}}x​+3y​5x​​

Use a calculator to approximate the square root. Round to three decimal places. - 11295\sqrt{\frac{112}{95}}95112​​

Add or subtract. Simplify by collecting like radical terms, if possible. - −5xy5x+xyx5+2yy5x-5 x \sqrt{y^{5} x}+x \sqrt{y x^{5}}+2 y \sqrt{y^{5} x}−5xy5x​+xyx5​+2yy5x​

Multiply and then, if possible, simplify by factoring. - 2x222x4\sqrt{2 x^{2}} \sqrt{22 x^{4}}2x2​22x4​

Simplify by factoring. - 490\sqrt{490}490​

Rationalize the denominator and simplify. - 914\frac{9}{\sqrt{14}}14​9​

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

Solve the problem. -The time TTT in seconds for a pendulum of length LLL feet to make one swing is given by T=2πL35T=2 \pi \sqrt{\frac{L}{35}}T=2π35L​​ . How long is a pendulum (to nearest hundredth) if it makes one swing in 1.5 seconds? Use 3.14 for π\piπ .