Question 1

Write the number as a product of a real number and $i$. Simplify the radical expression.
-$\sqrt{-4}$

Accepted Answer

A)  $2 \mathrm{i}$ 
B)  $-2 \mathrm{i}$ 
C)  $-\mathrm{i} \sqrt{2}$ 
D)  ± 2 
A)  $2 \mathrm{i}$ 
B)  $-2 \mathrm{i}$ 
C)  $-\mathrm{i} \sqrt{2}$ 
D)  ± 2

Question 2

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$

Accepted Answer

A)  $\sqrt[2]{x^{5}}$ 
B)  $\sqrt[63]{x^{10}}$ 
C)  $\sqrt[16]{x^{5}}$ 
D)  $\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$ 
A)  $\sqrt[2]{x^{5}}$ 
B)  $\sqrt[63]{x^{10}}$ 
C)  $\sqrt[16]{x^{5}}$ 
D)  $\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$

Question 3

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$6 \sqrt[3]{3}+12 \sqrt[3]{3}$

Accepted Answer

A)  $18 \sqrt[3]{6}$ 
B)  $6 \sqrt[3]{3}$ 
C)  $18 \sqrt[3]{9}$ 
D)  $18 \sqrt[3]{3}$ 
A)  $18 \sqrt[3]{6}$ 
B)  $6 \sqrt[3]{3}$ 
C)  $18 \sqrt[3]{9}$ 
D)  $18 \sqrt[3]{3}$

Question 4

Simplify the radical. Assume that all variables represent positive real numbers
-$\sqrt[3]{-\frac{125}{27}}$

Accepted Answer

A)  $\frac{5}{3}$ 
B)  $\frac{25}{9}$ 
C)  $-\frac{125}{27}$ 
D)  $-\frac{5}{3}$ 
A)  $\frac{5}{3}$ 
B)  $\frac{25}{9}$ 
C)  $-\frac{125}{27}$ 
D)  $-\frac{5}{3}$

Question 5

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$(8+8 \mathrm{i})-(-9+\mathrm{i})$

Accepted Answer

A)  $17+7 \mathrm{i}$ 
B)  $-17-7 \mathrm{i}$ 
C)  $-1+9 i$ 
D)  $17-7 \mathrm{i}$ 
A)  $17+7 \mathrm{i}$ 
B)  $-17-7 \mathrm{i}$ 
C)  $-1+9 i$ 
D)  $17-7 \mathrm{i}$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt[4]{t+4}=\sqrt[4]{9 t}$

Accepted Answer

A)  $\left\{\frac{4}{9}\right\}$ 
B)  $\{2\}$ 
C)  $\left\{\frac{1}{2}\right\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{4}{9}\right\}$ 
B)  $\{2\}$ 
C)  $\left\{\frac{1}{2}\right\}$ 
D)  $\varnothing$

Question 7

Find the decimal approximation for the radical. Round the answer to three decimal places.
-$\sqrt{6050}$

Accepted Answer

A)  77.779 
B)  6050.000 
C)  77.787 
D)  77.782 
A)  77.779 
B)  6050.000 
C)  77.787 
D)  77.782

Question 8

Find the equation of a circle satisfying the given conditions.
-Center: $(0,4)$; radius: 6

Accepted Answer

A)  $x^{2}+(y-4)^{2}=36$ 
B)  $(x+4)^{2}+y^{2}=36$ 
C)  $(x-4)^{2}+y^{2}=36$ 
D)  $x^{2}+(y+4)^{2}=6$ 
A)  $x^{2}+(y-4)^{2}=36$ 
B)  $(x+4)^{2}+y^{2}=36$ 
C)  $(x-4)^{2}+y^{2}=36$ 
D)  $x^{2}+(y+4)^{2}=6$

Question 9

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{\mathrm{x}}+2=0$

Accepted Answer

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

Question 10

Find the equation of a circle satisfying the given conditions.
-Center: $(1,-7)$; radius: 5

Accepted Answer

A)  $(x+7)^{2}+(y-1)^{2}=5$ 
B)  $(x-1)^{2}+(y+7)^{2}=25$ 
C)  $(x+1)^{2}+(y-7)^{2}=25$ 
D)  $(x-7)^{2}+(y+1)^{2}=5$ 
A)  $(x+7)^{2}+(y-1)^{2}=5$ 
B)  $(x-1)^{2}+(y+7)^{2}=25$ 
C)  $(x+1)^{2}+(y-7)^{2}=25$ 
D)  $(x-7)^{2}+(y+1)^{2}=5$

Question 11

Simplify the expression involving rational exponents.
-$9^{-3 / 2}$

Accepted Answer

A)  $\frac{1}{27}$ 
B)  Not a real number 
C)  $-\frac{27}{2}$ 
D)  -27 
A)  $\frac{1}{27}$ 
B)  Not a real number 
C)  $-\frac{27}{2}$ 
D)  -27

Question 12

Simplify the radical. Assume that all variables represent positive real numbers.
-$\sqrt[8]{x^{20}}$

Accepted Answer

A)  $x \sqrt{x}$ 
B)  $x^{2} \sqrt[8]{x^{4}}$ 
C)  $x^{2} \sqrt{x}$ 
D)  $x^{2} \sqrt[4]{x^{2}}$ 
A)  $x \sqrt{x}$ 
B)  $x^{2} \sqrt[8]{x^{4}}$ 
C)  $x^{2} \sqrt{x}$ 
D)  $x^{2} \sqrt[4]{x^{2}}$

Question 13

Graph the circle.
-$(x+4)^{2}+y^{2}=9$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Find the decimal approximation for the radical. Round the answer to three decimal places.
-$\sqrt{313}$

Accepted Answer

A)  17.697 
B)  313.000 
C)  17.689 
D)  17.692 
A)  17.697 
B)  313.000 
C)  17.689 
D)  17.692

Question 15

Write with radicals. Assume that all variables represent positive real numbers
-$\left(5 p y^{2}\right)^{1 / 3}$

Accepted Answer

A)  $\sqrt[5]{5 p y}$ 
B)  $\sqrt{5 p y^{2}}$ 
C)  $\sqrt[3]{5 p y}$ 
D)  $\sqrt[3]{5 p y^{2}}$ 
A)  $\sqrt[5]{5 p y}$ 
B)  $\sqrt{5 p y^{2}}$ 
C)  $\sqrt[3]{5 p y}$ 
D)  $\sqrt[3]{5 p y^{2}}$

Question 16

Find the unknown length in the right triangle. Simplify the answer if necessary.
-

Accepted Answer

A)  22 
B)  $2 \sqrt{119}$ 
C)  18 
D)  26 
A)  22 
B)  $2 \sqrt{119}$ 
C)  18 
D)  26

Question 17

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt[6]{64}$

Accepted Answer

A)  $\frac{32}{3}$ 
B)  12 
C)  -2 
D)  2 
A)  $\frac{32}{3}$ 
B)  12 
C)  -2 
D)  2

Question 18

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{2 x+5}-\sqrt{x-2}=3$

Accepted Answer

A)  $\{2\}$ 
B)  $\{3,8\}$ 
C)  $\{2,38\}$ 
D)  $\{-2\}$ 
A)  $\{2\}$ 
B)  $\{3,8\}$ 
C)  $\{2,38\}$ 
D)  $\{-2\}$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{p^{2}-5 p+9}=p-2$

Accepted Answer

A)  $\{3\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\{-5\}$ 
D)  $\{5\}$ 
A)  $\{3\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\{-5\}$ 
D)  $\{5\}$

Question 20

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$3 \mathrm{k}^{1 / 8}\left(-4 \mathrm{k}^{3 / 8}+6 \mathrm{k}^{3 / 4}\right)$

Accepted Answer

A)  $-12 k^{3 / 64}+18 k^{3 / 32}$ 
B)  $-12 \mathrm{k}^{-1 / 4}-18 \mathrm{k}^{-5 / 8}$ 
C)  $-12 \mathrm{k}^{1 / 2}+18 \mathrm{k}^{7 / 8}$ 
D)  $-12 \mathrm{k}^{1 / 2}-18 \mathrm{k}^{7 / 8}$ 
A)  $-12 k^{3 / 64}+18 k^{3 / 32}$ 
B)  $-12 \mathrm{k}^{-1 / 4}-18 \mathrm{k}^{-5 / 8}$ 
C)  $-12 \mathrm{k}^{1 / 2}+18 \mathrm{k}^{7 / 8}$ 
D)  $-12 \mathrm{k}^{1 / 2}-18 \mathrm{k}^{7 / 8}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-4}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $6 \sqrt[3]{3}+12 \sqrt[3]{3}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[3]{-\frac{125}{27}}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(8+8 \mathrm{i})-(-9+\mathrm{i})$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[4]{t+4}=\sqrt[4]{9 t}$

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt{6050}$

Find the equation of a circle satisfying the given conditions. -Center: $(0,4)$ ; radius: 6

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{x}}+2=0$

Find the equation of a circle satisfying the given conditions. -Center: $(1,-7)$ ; radius: 5

Simplify the expression involving rational exponents. - $9^{-3 / 2}$

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[8]{x^{20}}$

Graph the circle. - $(x+4)^{2}+y^{2}=9$ $Graph the circle. - (x+4)^{2}+y^{2}=9$

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt{313}$

Write with radicals. Assume that all variables represent positive real numbers - $\left(5 p y^{2}\right)^{1 / 3}$

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt[6]{64}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{2 x+5}-\sqrt{x-2}=3$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{p^{2}-5 p+9}=p-2$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $3 \mathrm{k}^{1 / 8}\left(-4 \mathrm{k}^{3 / 8}+6 \mathrm{k}^{3 / 4}\right)$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 8: Roots, Radicals, and Root Functions

Write the number as a product of a real number and iii . Simplify the radical expression. - −4\sqrt{-4}−4​

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - x57x59\frac{\sqrt[7]{x^{5}}}{\sqrt[9]{x^{5}}}9x5​7x5​​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 633+12336 \sqrt[3]{3}+12 \sqrt[3]{3}633​+1233​

Simplify the radical. Assume that all variables represent positive real numbers - −125273\sqrt[3]{-\frac{125}{27}}3−27125​​

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - (8+8i)−(−9+i)(8+8 \mathrm{i})-(-9+\mathrm{i})(8+8i)−(−9+i)

Choose the one alternative that best completes the statement or answers the question. Solve the equation - t+44=9t4\sqrt[4]{t+4}=\sqrt[4]{9 t}4t+4​=49t​

Find the decimal approximation for the radical. Round the answer to three decimal places. - 6050\sqrt{6050}6050​

Find the equation of a circle satisfying the given conditions. -Center: (0,4)(0,4)(0,4) ; radius: 6

Choose the one alternative that best completes the statement or answers the question. Solve the equation - x+2=0\sqrt{\mathrm{x}}+2=0x​+2=0

Find the equation of a circle satisfying the given conditions. -Center: (1,−7)(1,-7)(1,−7) ; radius: 5

Simplify the expression involving rational exponents. - 9−3/29^{-3 / 2}9−3/2

Simplify the radical. Assume that all variables represent positive real numbers. - x208\sqrt[8]{x^{20}}8x20​

Graph the circle. - (x+4)2+y2=9(x+4)^{2}+y^{2}=9(x+4)2+y2=9

Find the decimal approximation for the radical. Round the answer to three decimal places. - 313\sqrt{313}313​

Write with radicals. Assume that all variables represent positive real numbers - (5py2)1/3\left(5 p y^{2}\right)^{1 / 3}(5py2)1/3