Question 1

Multiply and then, if possible, simplify by factoring.
-$\sqrt{x^{4} y^{2}} \sqrt{x y^{9}}$

Accepted Answer

A)  $x^{4} y 10 \sqrt{x y}$ 
B)  $\sqrt{x^{5} y^{11}}$ 
C)  $x^{2} y^{5} \sqrt{x y}$ 
D)  $x^{2} \sqrt{x y^{11}}$ 
A)  $x^{4} y 10 \sqrt{x y}$ 
B)  $\sqrt{x^{5} y^{11}}$ 
C)  $x^{2} y^{5} \sqrt{x y}$ 
D)  $x^{2} \sqrt{x y^{11}}$ C

Question 2

Solve the problem. Give an exact answer and an approximation to the nearest tenth.
-The diagram below shows a rope connecting the top of a pole to the ground. How tall is the pole?

Accepted Answer

A)  $\sqrt{4} \mathrm{yd} \approx 2.0 \mathrm{yd}$ 
B)  $\sqrt{216} \mathrm{yd} \approx 14.7 \mathrm{yd}$ 
C)  $\sqrt{1466} y d \approx 38.3 y d$ 
D)  $\sqrt{216} \mathrm{yd}=108 \mathrm{yd}$ 
A)  $\sqrt{4} \mathrm{yd} \approx 2.0 \mathrm{yd}$ 
B)  $\sqrt{216} \mathrm{yd} \approx 14.7 \mathrm{yd}$ 
C)  $\sqrt{1466} y d \approx 38.3 y d$ 
D)  $\sqrt{216} \mathrm{yd}=108 \mathrm{yd}$ B

Question 3

Provide an appropriate response.
-Is $\sqrt{25}=5$ ?

Accepted Answer

A) True 
 B)False  True

Question 4

Multiply and then, if possible, simplify by factoring.
-$\sqrt{7 x} \sqrt{2401 y}$

Accepted Answer

A)  $49 x y$ 
B)  $\sqrt{2401 x y}$ 
C)  $2401 \sqrt{x y}$ 
D)  $49 \sqrt{7 \mathrm{xy}}$ 
A)  $49 x y$ 
B)  $\sqrt{2401 x y}$ 
C)  $2401 \sqrt{x y}$ 
D)  $49 \sqrt{7 \mathrm{xy}}$

Question 5

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

Accepted Answer

A)  $-1 \sqrt{7}$ 
B)  $-7 \sqrt{7}$ 
C)  $6 \sqrt{7}$ 
D)  $2 \sqrt{7}$ 
A)  $-1 \sqrt{7}$ 
B)  $-7 \sqrt{7}$ 
C)  $6 \sqrt{7}$ 
D)  $2 \sqrt{7}$

Question 6

Solve the equation.
-$\sqrt{q+3}=8$

Accepted Answer

A)  64 
B)  67 
C)  61 
D)  121 
A)  64 
B)  67 
C)  61 
D)  121

Question 7

Provide an appropriate response.
-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 id

Question 8

Simplify.
-$\sqrt{\frac{27 \mathrm{x}^{2}}{25}}$

Accepted Answer

A)  $x \sqrt{\frac{27}{5}}$ 
B)  $\frac{3 \sqrt{3 x^{2}}}{5}$ 
C)  $\frac{3 x \sqrt{3}}{5}$ 
D)  $9 x \sqrt{3}$ 
A)  $x \sqrt{\frac{27}{5}}$ 
B)  $\frac{3 \sqrt{3 x^{2}}}{5}$ 
C)  $\frac{3 x \sqrt{3}}{5}$ 
D)  $9 x \sqrt{3}$

Question 9

Rationalize the denominator and simplify.
-$\sqrt{\frac{98}{\mathrm{x}}}$

Accepted Answer

A)  $\frac{7 \sqrt{2 x}}{x}$ 
B)  $\frac{\sqrt{7 x}}{x}$ 
C)  $7 \sqrt{2 x}$ 
D)  $7 \sqrt{\frac{2}{\mathrm{x}}}$ 
A)  $\frac{7 \sqrt{2 x}}{x}$ 
B)  $\frac{\sqrt{7 x}}{x}$ 
C)  $7 \sqrt{2 x}$ 
D)  $7 \sqrt{\frac{2}{\mathrm{x}}}$

Question 10

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{z^{2}-10 z+25}$

Accepted Answer

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

Question 11

Rationalize the denominator and simplify.
-$\frac{\sqrt{3}+1}{4+\sqrt{2}}$

Accepted Answer

A)  $\frac{\sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14}$ 
B)  $\frac{4 \sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14+8 \sqrt{2}}$ 
C)  $\frac{4 \sqrt{3}+\sqrt{6}+4+\sqrt{2}}{14}$ 
D)  $\frac{4 \sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14}$ 
A)  $\frac{\sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14}$ 
B)  $\frac{4 \sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14+8 \sqrt{2}}$ 
C)  $\frac{4 \sqrt{3}+\sqrt{6}+4+\sqrt{2}}{14}$ 
D)  $\frac{4 \sqrt{3}-\sqrt{6}+4-\sqrt{2}}{14}$

Question 12

Rationalize the denominator and simplify.
-$\frac{\sqrt{7}+9}{\sqrt{3}+3}$

Accepted Answer

A)  $\frac{\sqrt{21}+27+9 \sqrt{3}+3 \sqrt{7}}{12}$ 
B)  $\frac{\sqrt{21}+27+9 \sqrt{3}+3 \sqrt{7}}{6}$ 
C)  $\frac{\sqrt{21}-27+9 \sqrt{3}-3 \sqrt{7}}{12}$ 
D)  $\frac{-\sqrt{21}+27-9 \sqrt{3}+3 \sqrt{7}}{6}$ 
A)  $\frac{\sqrt{21}+27+9 \sqrt{3}+3 \sqrt{7}}{12}$ 
B)  $\frac{\sqrt{21}+27+9 \sqrt{3}+3 \sqrt{7}}{6}$ 
C)  $\frac{\sqrt{21}-27+9 \sqrt{3}-3 \sqrt{7}}{12}$ 
D)  $\frac{-\sqrt{21}+27-9 \sqrt{3}+3 \sqrt{7}}{6}$

Question 13

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

Accepted Answer

A)  $\sqrt{6}$ 
B)  1 
C)  6 
D)  $6 \sqrt{6}$ 
A)  $\sqrt{6}$ 
B)  1 
C)  6 
D)  $6 \sqrt{6}$

Question 14

Solve the problem. Give an exact answer and an approximation to the nearest tenth.
-A painter leans a ladder against one wall of a house. At what height does the ladder touch the wall?

Accepted Answer

A)  $\sqrt{363} \mathrm{ft} \approx 19.1 \mathrm{ft}$ 
B)  $\sqrt{605} \mathrm{ft} \approx 24.6 \mathrm{ft}$ 
C)  $\sqrt{11} \mathrm{ft} \approx 3.3 \mathrm{ft}$ 
D)  $\sqrt{363} \mathrm{ft}=181.5 \mathrm{ft}$ 
A)  $\sqrt{363} \mathrm{ft} \approx 19.1 \mathrm{ft}$ 
B)  $\sqrt{605} \mathrm{ft} \approx 24.6 \mathrm{ft}$ 
C)  $\sqrt{11} \mathrm{ft} \approx 3.3 \mathrm{ft}$ 
D)  $\sqrt{363} \mathrm{ft}=181.5 \mathrm{ft}$

Question 15

Identify the radicand.
-$x y^{2} \sqrt{\frac{5}{x+6}}$

Accepted Answer

A)  $x y^{2}$ 
B)  $x+6$ 
C)  $\frac{5}{x+6}$ 
D)  $\sqrt{\frac{5}{x+6}}$ 
A)  $x y^{2}$ 
B)  $x+6$ 
C)  $\frac{5}{x+6}$ 
D)  $\sqrt{\frac{5}{x+6}}$

Question 16

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)  $\sqrt{128} \approx 11.314$ 
B)  16 
C)  8 
D)  $\sqrt{192} \approx 13.856$ 
A)  $\sqrt{128} \approx 11.314$ 
B)  16 
C)  8 
D)  $\sqrt{192} \approx 13.856$

Question 17

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)  18 
B)  13 
C)  25 
D)  24 
A)  18 
B)  13 
C)  25 
D)  24

Question 18

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{(15 y)^{2}}$

Accepted Answer

A)  $225 y^{2}$ 
B)  $\mathrm{y}$ 
C)  $225 y$ 
D)  $15 y$ 
A)  $225 y^{2}$ 
B)  $\mathrm{y}$ 
C)  $225 y$ 
D)  $15 y$

Question 19

Perform the indicated operation.
-$\sqrt{3}(\sqrt{7}-\sqrt{5})$

Accepted Answer

A)  6 
B)  $\sqrt{21}-\sqrt{15}$ 
C)  $3 \sqrt{7}+3 \sqrt{5}$ 
D)  $12 \sqrt{3}$ 
A)  6 
B)  $\sqrt{21}-\sqrt{15}$ 
C)  $3 \sqrt{7}+3 \sqrt{5}$ 
D)  $12 \sqrt{3}$

Question 20

Identify the radicand.
-$s^{2} t \sqrt{\frac{s}{s-5 t}}$

Accepted Answer

A)  $\sqrt{\frac{s}{s-5 t}}$ 
B)  $\frac{s}{s-5 t}$ 
C)  $\left(s^{2} t\right) \frac{s}{s-5 t}$ 
D)  $s^{2} t$ 
A)  $\sqrt{\frac{s}{s-5 t}}$ 
B)  $\frac{s}{s-5 t}$ 
C)  $\left(s^{2} t\right) \frac{s}{s-5 t}$ 
D)  $s^{2} t$

Multiply and then, if possible, simplify by factoring. - $\sqrt{x^{4} y^{2}} \sqrt{x y^{9}}$

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -The diagram below shows a rope connecting the top of a pole to the ground. How tall is the pole?

Provide an appropriate response. -Is $\sqrt{25}=5$ ?

Multiply and then, if possible, simplify by factoring. - $\sqrt{7 x} \sqrt{2401 y}$

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

Solve the equation. - $\sqrt{q+3}=8$

Provide an appropriate response. -Why should you simplify each term in a radical expression before attempting to collect like radical terms?

Simplify. - $\sqrt{\frac{27 \mathrm{x}^{2}}{25}}$

Rationalize the denominator and simplify. - $\sqrt{\frac{98}{\mathrm{x}}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{z^{2}-10 z+25}$

Rationalize the denominator and simplify. - $\frac{\sqrt{3}+1}{4+\sqrt{2}}$

Rationalize the denominator and simplify. - $\frac{\sqrt{7}+9}{\sqrt{3}+3}$

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

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -A painter leans a ladder against one wall of a house. At what height does the ladder touch the wall?

Identify the radicand. - $x y^{2} \sqrt{\frac{5}{x+6}}$

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. -

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. -

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{(15 y)^{2}}$

Perform the indicated operation. - $\sqrt{3}(\sqrt{7}-\sqrt{5})$

Identify the radicand. - $s^{2} t \sqrt{\frac{s}{s-5 t}}$

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

Multiply and then, if possible, simplify by factoring. - x4y2xy9\sqrt{x^{4} y^{2}} \sqrt{x y^{9}}x4y2​xy9​

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -The diagram below shows a rope connecting the top of a pole to the ground. How tall is the pole?

Provide an appropriate response. -Is 25=5\sqrt{25}=525​=5 ?

Multiply and then, if possible, simplify by factoring. - 7x2401y\sqrt{7 x} \sqrt{2401 y}7x​2401y​

Add or subtract. Simplify by collecting like radical terms, if possible. - −47−37-4 \sqrt{7}-3 \sqrt{7}−47​−37​

Solve the equation. - q+3=8\sqrt{q+3}=8q+3​=8

Provide an appropriate response. -Why should you simplify each term in a radical expression before attempting to collect like radical terms?

Simplify. - 27x225\sqrt{\frac{27 \mathrm{x}^{2}}{25}}2527x2​​

Rationalize the denominator and simplify. - 98x\sqrt{\frac{98}{\mathrm{x}}}x98​​

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - z2−10z+25\sqrt{z^{2}-10 z+25}z2−10z+25​

Rationalize the denominator and simplify. - 3+14+2\frac{\sqrt{3}+1}{4+\sqrt{2}}4+2​3​+1​

Rationalize the denominator and simplify. - 7+93+3\frac{\sqrt{7}+9}{\sqrt{3}+3}3​+37​+9​

Rationalize the denominator and simplify. - 66\frac{6}{\sqrt{6}}6​6​

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -A painter leans a ladder against one wall of a house. At what height does the ladder touch the wall?

Identify the radicand. - xy25x+6x y^{2} \sqrt{\frac{5}{x+6}}xy2x+65​​

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. -

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. -

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - (15y)2\sqrt{(15 y)^{2}}(15y)2​

Perform the indicated operation. - 3(7−5)\sqrt{3}(\sqrt{7}-\sqrt{5})3​(7​−5​)

Identify the radicand. - s2tss−5ts^{2} t \sqrt{\frac{s}{s-5 t}}s2ts−5ts​​

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

Multiply and then, if possible, simplify by factoring. - $\sqrt{x^{4} y^{2}} \sqrt{x y^{9}}$

Provide an appropriate response. -Is $\sqrt{25}=5$ ?

Multiply and then, if possible, simplify by factoring. - $\sqrt{7 x} \sqrt{2401 y}$

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

Solve the equation. - $\sqrt{q+3}=8$

Simplify. - $\sqrt{\frac{27 \mathrm{x}^{2}}{25}}$

Rationalize the denominator and simplify. - $\sqrt{\frac{98}{\mathrm{x}}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{z^{2}-10 z+25}$

Rationalize the denominator and simplify. - $\frac{\sqrt{3}+1}{4+\sqrt{2}}$

Rationalize the denominator and simplify. - $\frac{\sqrt{7}+9}{\sqrt{3}+3}$

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

Identify the radicand. - $x y^{2} \sqrt{\frac{5}{x+6}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{(15 y)^{2}}$

Perform the indicated operation. - $\sqrt{3}(\sqrt{7}-\sqrt{5})$

Identify the radicand. - $s^{2} t \sqrt{\frac{s}{s-5 t}}$