Question 1

Find the equation of a circle satisfying the given conditions.
-Center: $(-10,2)$; radius: 1

Accepted Answer

A)  $(x+2)^{2}+(y-10)^{2}=1$ 
B)  $(x-2)^{2}+(y+10)^{2}=1$ 
C)  $(x-10)^{2}+(y+2)^{2}=1$ 
D)  $(x+10)^{2}+(y-2)^{2}=1$ 
A)  $(x+2)^{2}+(y-10)^{2}=1$ 
B)  $(x-2)^{2}+(y+10)^{2}=1$ 
C)  $(x-10)^{2}+(y+2)^{2}=1$ 
D)  $(x+10)^{2}+(y-2)^{2}=1$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt[3]{5 x^{2}+6 x+1}=\sqrt[3]{5 x^{2}+7 x+9}$

Accepted Answer

A)  $\{8\}$ 
B)  $\left\{\frac{1}{8}\right\}$ 
C)  $\left\{-\frac{1}{8}\right\}$ 
D)  $\{-8\}$ 
A)  $\{8\}$ 
B)  $\left\{\frac{1}{8}\right\}$ 
C)  $\left\{-\frac{1}{8}\right\}$ 
D)  $\{-8\}$

Question 3

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation.
-$(10+x)^{1 / 2}+(11-5 x)^{1 / 2}=-1$

Accepted Answer

A)  $\varnothing$ 
B)  $\{0\}$ 
C)  $\left\{-1, \frac{10}{9}\right\}$ 
D)  $\{1\}$ 
A)  $\varnothing$ 
B)  $\{0\}$ 
C)  $\left\{-1, \frac{10}{9}\right\}$ 
D)  $\{1\}$

Question 4

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$10 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}$

Accepted Answer

A)  $5 x \sqrt[4]{x^{7}}$ 
B)  $15 \sqrt[4]{x^{3}}$ 
C)  $10 \sqrt[4]{x^{7}}-5 x \sqrt[4]{x^{3}}$ 
D)  $5 x \sqrt[4]{x^{3}}$ 
A)  $5 x \sqrt[4]{x^{7}}$ 
B)  $15 \sqrt[4]{x^{3}}$ 
C)  $10 \sqrt[4]{x^{7}}-5 x \sqrt[4]{x^{3}}$ 
D)  $5 x \sqrt[4]{x^{3}}$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{\mathrm{q}+2}=4$

Accepted Answer

A)  $\{16\}$ 
B)  $\{18\}$ 
C)  $\{14\}$ 
D)  $\{36\}$ 
A)  $\{16\}$ 
B)  $\{18\}$ 
C)  $\{14\}$ 
D)  $\{36\}$

Question 6

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[3]{-27 a^{8} b^{5}}$

Accepted Answer

A)  $3 a b \sqrt[3]{a^{3} b^{3}}$ 
B)  $3 a b \sqrt[3]{a^{2} b^{2}}$ 
C)  $3 \sqrt[3]{a^{2} b^{2}}$ 
D)  $-3 a^{2} b \sqrt[3]{a^{2} b^{2}}$ 
A)  $3 a b \sqrt[3]{a^{3} b^{3}}$ 
B)  $3 a b \sqrt[3]{a^{2} b^{2}}$ 
C)  $3 \sqrt[3]{a^{2} b^{2}}$ 
D)  $-3 a^{2} b \sqrt[3]{a^{2} b^{2}}$

Question 7

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form.
-$\sqrt[4]{x^{7}} \cdot \sqrt[3]{x^{2}}$

Accepted Answer

A)  $x^{12 / 14}$ 
B)  $x^{14 / 12}$ 
C)  $x^{29 / 12}$ 
D)  $x^{9 / 7}$ 
A)  $x^{12 / 14}$ 
B)  $x^{14 / 12}$ 
C)  $x^{29 / 12}$ 
D)  $x^{9 / 7}$

Question 8

Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$(\sqrt{13}+1)(\sqrt{13}-1)$

Accepted Answer

A)  $12-2 \sqrt{13}$ 
B)  14 
C)  12 
D)  $12+2 \sqrt{13}$ 
A)  $12-2 \sqrt{13}$ 
B)  14 
C)  12 
D)  $12+2 \sqrt{13}$

Question 9

Solve the equation.
-$\sqrt{x+6}+\sqrt{2-x}=4$

Accepted Answer

A)  $\{0\}$ 
B)  $\{2,-2\}$ 
C)  $\{-2\}$ 
D)  $\{\sqrt{31},-2\}$ 
A)  $\{0\}$ 
B)  $\{2,-2\}$ 
C)  $\{-2\}$ 
D)  $\{\sqrt{31},-2\}$

Question 10

Rationalize the denominator. Assume that all variables represent positive real numbers. 
-$\frac{4 z}{\sqrt{11}}$

Accepted Answer

A)  $\frac{4 z \sqrt{11}}{11}$ 
B)  125 
C)  $4 z \sqrt{11}$ 
D)  $\frac{16 z \sqrt{11}}{11}$ 
A)  $\frac{4 z \sqrt{11}}{11}$ 
B)  125 
C)  $4 z \sqrt{11}$ 
D)  $\frac{16 z \sqrt{11}}{11}$

Question 11

Graph the function and give its domain and its range.
-$f(x)=\sqrt{x}+1$

Accepted Answer

A)  $ [-1, \infty) $; $ [0, \infty) $
  
B)  $ [0, \infty) $; $ [-1, \infty) $
  
C)  $ [1, \infty) ;[0, \infty) $
  
D)  $ [0, \infty) ;[1, \infty) $
  
A)  $ [-1, \infty) $; $ [0, \infty) $
  
B)  $ [0, \infty) $; $ [-1, \infty) $
  
C)  $ [1, \infty) ;[0, \infty) $
  
D)  $ [0, \infty) ;[1, \infty) $

Question 12

Choose the one alternative that best completes the statement or answers the question.
-A rectangle has a length of $\sqrt{252}$ and a width of $\sqrt{221}$. What is the best estimate for its area?

Accepted Answer

A)  225 
B)  210 
C)  224 
D)  240 
A)  225 
B)  210 
C)  224 
D)  240

Question 13

Rationalize the denominator. Assume that all variables represent positive real numbers. 
-$\frac{9}{\sqrt{7}}$

Accepted Answer

A)  58 
B)  $\frac{81 \sqrt{7}}{7}$ 
C)  $9 \sqrt{7}$ 
D)  $\frac{9 \sqrt{7}}{7}$ 
A)  58 
B)  $\frac{81 \sqrt{7}}{7}$ 
C)  $9 \sqrt{7}$ 
D)  $\frac{9 \sqrt{7}}{7}$

Question 14

Simplify the expression. Assume that all variables represent positive real numbers.
-$\left(\frac{25}{9}\right)^{-3 / 2}$

Accepted Answer

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

Question 15

Choose the one alternative that best completes the statement or answers the question.
Multiply using the product rule.
-$\sqrt[4]{5} \cdot \sqrt[4]{25}$

Accepted Answer

A)  5 
B)  $\sqrt[8]{30}$ 
C)  $\sqrt[4]{125}$ 
D)  $\sqrt[4]{30}$ 
A)  5 
B)  $\sqrt[8]{30}$ 
C)  $\sqrt[4]{125}$ 
D)  $\sqrt[4]{30}$

Question 16

Simplify the radical. Assume that all variables represent positive real numbers
-$\sqrt[3]{\frac{1296 \mathrm{x}^{4}}{6 \mathrm{x}}}$

Accepted Answer

A)  $6 x \sqrt[3]{6}$ 
B)  $x \sqrt[3]{216}$ 
C)  $6 x$ 
D)  $6 x \sqrt[3]{x}$ 
A)  $6 x \sqrt[3]{6}$ 
B)  $x \sqrt[3]{216}$ 
C)  $6 x$ 
D)  $6 x \sqrt[3]{x}$

Question 17

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$(-8+7 \mathrm{i})-6$

Accepted Answer

A)  $14-7 \mathrm{i}$ 
B)  $-2-7 \mathrm{i}$ 
C)  $-14+7 i$ 
D)  $-2+7 i$ 
A)  $14-7 \mathrm{i}$ 
B)  $-2-7 \mathrm{i}$ 
C)  $-14+7 i$ 
D)  $-2+7 i$

Question 18

Simplify. Assume that all variables represent positive real numbers.
-$-\sqrt[3]{\frac{2 \mathrm{x}}{\mathrm{y}}}$

Accepted Answer

A)  $-\frac{\sqrt[3]{2 x^{2} y^{2}}}{y}$ 
B)  $-\frac{\sqrt[3]{2 x^{2} y}}{y}$ 
C)  $-\frac{\sqrt[3]{2 x y^{2}}}{y}$ 
D)  $-\frac{\sqrt[3]{2 x y}}{y}$ 
A)  $-\frac{\sqrt[3]{2 x^{2} y^{2}}}{y}$ 
B)  $-\frac{\sqrt[3]{2 x^{2} y}}{y}$ 
C)  $-\frac{\sqrt[3]{2 x y^{2}}}{y}$ 
D)  $-\frac{\sqrt[3]{2 x y}}{y}$

Question 19

Simplify the expression involving rational exponents.
-$(-4)^{1 / 2}$

Accepted Answer

A)  -1 
B)  -2 
C)  Not a real number 
D)  2 
A)  -1 
B)  -2 
C)  Not a real number 
D)  2

Question 20

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[3]{1080}$

Accepted Answer

A)  10 
B)  $6 \sqrt[3]{5}$ 
C)  32 
D)  $5 \sqrt[3]{6}$ 
A)  10 
B)  $6 \sqrt[3]{5}$ 
C)  32 
D)  $5 \sqrt[3]{6}$

Find the equation of a circle satisfying the given conditions. -Center: $(-10,2)$ ; radius: 1

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[3]{5 x^{2}+6 x+1}=\sqrt[3]{5 x^{2}+7 x+9}$

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $(10+x)^{1 / 2}+(11-5 x)^{1 / 2}=-1$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $10 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{q}+2}=4$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{-27 a^{8} b^{5}}$

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. - $\sqrt[4]{x^{7}} \cdot \sqrt[3]{x^{2}}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(\sqrt{13}+1)(\sqrt{13}-1)$

Solve the equation. - $\sqrt{x+6}+\sqrt{2-x}=4$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{4 z}{\sqrt{11}}$

Graph the function and give its domain and its range. - $f(x)=\sqrt{x}+1$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x}+1$

Choose the one alternative that best completes the statement or answers the question. -A rectangle has a length of $\sqrt{252}$ and a width of $\sqrt{221}$ . What is the best estimate for its area?

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9}{\sqrt{7}}$

Simplify the expression. Assume that all variables represent positive real numbers. - $\left(\frac{25}{9}\right)^{-3 / 2}$

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - $\sqrt[4]{5} \cdot \sqrt[4]{25}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[3]{\frac{1296 \mathrm{x}^{4}}{6 \mathrm{x}}}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(-8+7 \mathrm{i})-6$

Simplify. Assume that all variables represent positive real numbers. - $-\sqrt[3]{\frac{2 \mathrm{x}}{\mathrm{y}}}$

Simplify the expression involving rational exponents. - $(-4)^{1 / 2}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{1080}$

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

Find the equation of a circle satisfying the given conditions. -Center: (−10,2)(-10,2)(−10,2) ; radius: 1

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 5x2+6x+13=5x2+7x+93\sqrt[3]{5 x^{2}+6 x+1}=\sqrt[3]{5 x^{2}+7 x+9}35x2+6x+1​=35x2+7x+9​

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - (10+x)1/2+(11−5x)1/2=−1(10+x)^{1 / 2}+(11-5 x)^{1 / 2}=-1(10+x)1/2+(11−5x)1/2=−1

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 10x74−5xx3410 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}104x7​−5x4x3​

Choose the one alternative that best completes the statement or answers the question. Solve the equation - q+2=4\sqrt{\mathrm{q}+2}=4q+2​=4

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −27a8b53\sqrt[3]{-27 a^{8} b^{5}}3−27a8b5​

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. - x74⋅x23\sqrt[4]{x^{7}} \cdot \sqrt[3]{x^{2}}4x7​⋅3x2​

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - (13+1)(13−1)(\sqrt{13}+1)(\sqrt{13}-1)(13​+1)(13​−1)

Solve the equation. - x+6+2−x=4\sqrt{x+6}+\sqrt{2-x}=4x+6​+2−x​=4

Rationalize the denominator. Assume that all variables represent positive real numbers. - 4z11\frac{4 z}{\sqrt{11}}11​4z​

Graph the function and give its domain and its range. - f(x)=x+1f(x)=\sqrt{x}+1f(x)=x​+1

Choose the one alternative that best completes the statement or answers the question. -A rectangle has a length of 252\sqrt{252}252​ and a width of 221\sqrt{221}221​ . What is the best estimate for its area?

Rationalize the denominator. Assume that all variables represent positive real numbers. - 97\frac{9}{\sqrt{7}}7​9​

Simplify the expression. Assume that all variables represent positive real numbers. - (259)−3/2\left(\frac{25}{9}\right)^{-3 / 2}(925​)−3/2

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - 54⋅254\sqrt[4]{5} \cdot \sqrt[4]{25}45​⋅425​

Simplify the radical. Assume that all variables represent positive real numbers - 1296x46x3\sqrt[3]{\frac{1296 \mathrm{x}^{4}}{6 \mathrm{x}}}36x1296x4​​

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - (−8+7i)−6(-8+7 \mathrm{i})-6(−8+7i)−6

Simplify. Assume that all variables represent positive real numbers. - −2xy3-\sqrt[3]{\frac{2 \mathrm{x}}{\mathrm{y}}}−3y2x​​

Simplify the expression involving rational exponents. - (−4)1/2(-4)^{1 / 2}(−4)1/2

Express the radical in simplified form.Assume that all variables represent positive real numbers. - 10803\sqrt[3]{1080}31080​