Question 1

Simplify by factoring.
-$\sqrt{\mathrm{x}^{6}}$

Accepted Answer

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

Question 2

Multiply and then, if possible, simplify by factoring.
-$\sqrt{5 x} \sqrt{15 x}$

Accepted Answer

A)  $5 x \sqrt{3}$ 
B)  $5 \sqrt{3 x}$ 
C)  $25 x \sqrt{3}$ 
D)  $\sqrt{75 x^{2}}$ 
A)  $5 x \sqrt{3}$ 
B)  $5 \sqrt{3 x}$ 
C)  $25 x \sqrt{3}$ 
D)  $\sqrt{75 x^{2}}$

Question 3

Simplify by factoring.
-$-\sqrt{432}$

Accepted Answer

A)  -20 
B)  -72 
C)  $-12 \sqrt{6}$ 
D)  $-12 \sqrt{3}$ 
A)  -20 
B)  -72 
C)  $-12 \sqrt{6}$ 
D)  $-12 \sqrt{3}$

Question 4

Decide whether or not the radical expression represents a real number.
-$\sqrt{16}$

Accepted Answer

A) True 
 B)False

Question 5

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{25 x^{2}+30 x+9}$

Accepted Answer

A)  none of these 
B)  $(5 \mathrm{x}+3)^{2}$ 
C)  $5 x+3$ 
D)  $\sqrt{(5 x+3)^{2}}$ 
A)  none of these 
B)  $(5 \mathrm{x}+3)^{2}$ 
C)  $5 x+3$ 
D)  $\sqrt{(5 x+3)^{2}}$

Question 6

Add or subtract. Simplify by collecting like radical terms, if possible.
-$4 \sqrt{5}+\frac{-2}{\sqrt{5}}$

Accepted Answer

A)  $\frac{18 \sqrt{5}}{5 \sqrt{5}}$ 
B)  $18 \sqrt{5}$ 
C)  $\frac{18 \sqrt{5}}{5}$ 
D)  $2 \sqrt{5}$ 
A)  $\frac{18 \sqrt{5}}{5 \sqrt{5}}$ 
B)  $18 \sqrt{5}$ 
C)  $\frac{18 \sqrt{5}}{5}$ 
D)  $2 \sqrt{5}$

Question 7

Provide an appropriate response.
-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 8

Perform the indicated operation.
-$6 \sqrt{5}(\sqrt{11}+\sqrt{5})$

Accepted Answer

A)  $6 \sqrt{55}+5$ 
B)  $6 \sqrt{55}+30$ 
C)  $6 \sqrt{11}+5$ 
D)  $30 \sqrt{11}+30$ 
A)  $6 \sqrt{55}+5$ 
B)  $6 \sqrt{55}+30$ 
C)  $6 \sqrt{11}+5$ 
D)  $30 \sqrt{11}+30$

Question 9

Provide an appropriate response.
-Is $\sqrt{11}$ simplified?

Accepted Answer

A) True 
 B)False

Question 10

Simplify by factoring.
-$\sqrt{75 x^{2}}$

Accepted Answer

A)  $75 x$ 
B)  $5 \sqrt{3 x}$ 
C)  $5 x \sqrt{3}$ 
D)  $3 x^{2} \sqrt{5}$ 
A)  $75 x$ 
B)  $5 \sqrt{3 x}$ 
C)  $5 x \sqrt{3}$ 
D)  $3 x^{2} \sqrt{5}$

Question 11

Solve the equation.
-$\sqrt{2 \mathrm{x}+3}-\sqrt{\mathrm{x}+1}=1$

Accepted Answer

A)  3 
B)  No solution 
C)  $-3,-1$ 
D)  $3,-1$ 
A)  3 
B)  No solution 
C)  $-3,-1$ 
D)  $3,-1$

Question 12

Solve the equation.
-$\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

Accepted Answer

A)  3,8 
B)  2,38 
C)  -2 
D)  2 
A)  3,8 
B)  2,38 
C)  -2 
D)  2

Question 13

Divide and simplify.
-$\frac{\sqrt{20}}{\sqrt{5}}$

Accepted Answer

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

Question 14

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

Accepted Answer

A)  $\frac{-\sqrt{14}+14-7 \sqrt{2}+2 \sqrt{7}}{2}$ 
B)  $\frac{\sqrt{14}-14+7 \sqrt{2}-2 \sqrt{7}}{6}$ 
C)  $\frac{\sqrt{14}+14+7 \sqrt{2}+2 \sqrt{7}}{2}$ 
D)  $\frac{\sqrt{14}+14+7 \sqrt{2}+2 \sqrt{7}}{6}$ 
A)  $\frac{-\sqrt{14}+14-7 \sqrt{2}+2 \sqrt{7}}{2}$ 
B)  $\frac{\sqrt{14}-14+7 \sqrt{2}-2 \sqrt{7}}{6}$ 
C)  $\frac{\sqrt{14}+14+7 \sqrt{2}+2 \sqrt{7}}{2}$ 
D)  $\frac{\sqrt{14}+14+7 \sqrt{2}+2 \sqrt{7}}{6}$

Question 15

Simplify.
-$\sqrt{\frac{100}{49}}$

Accepted Answer

A)  $\frac{\sqrt{10}}{\sqrt{7}}$ 
B)  $\frac{\sqrt{10}}{7}$ 
C)  $\frac{10}{7}$ 
D)  1 
A)  $\frac{\sqrt{10}}{\sqrt{7}}$ 
B)  $\frac{\sqrt{10}}{7}$ 
C)  $\frac{10}{7}$ 
D)  1

Question 16

Simplify by factoring.
-$\sqrt{486 y^{2}}$

Accepted Answer

A)  $9 y \sqrt{6}$ 
B)  $9 \sqrt{6 y^{2}}$ 
C)  $9 \sqrt{6}$ 
D)  $9 y^{2} \sqrt{6}$ 
A)  $9 y \sqrt{6}$ 
B)  $9 \sqrt{6 y^{2}}$ 
C)  $9 \sqrt{6}$ 
D)  $9 y^{2} \sqrt{6}$

Question 17

Provide an appropriate response.
-If $\mathrm{p}$ is a prime number, is $\sqrt{\mathrm{p}}$ in simplified form? Explain.

Accepted Answer

A) True 
 B)False

Question 18

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.
-$a=30, c=50$

Accepted Answer

A)  $b=80$ 
B)  $b=20$ 
C)  $b=10$ 
D)  $b=40$ 
A)  $b=80$ 
B)  $b=20$ 
C)  $b=10$ 
D)  $b=40$

Question 19

Simplify.
-$\sqrt{\frac{19}{\mathrm{x}^{4} \mathrm{y}^{4}}}$

Accepted Answer

A)  $\frac{\sqrt{19}}{x^{2} y^{2}}$ 
B)  $\frac{\sqrt{19 x^{4} y^{4}}}{x^{4} y^{4}}$ 
C)  $\frac{\sqrt{19}}{x^{4} y^{4}}$ 
D)  $\frac{\sqrt{19}}{x y}$ 
A)  $\frac{\sqrt{19}}{x^{2} y^{2}}$ 
B)  $\frac{\sqrt{19 x^{4} y^{4}}}{x^{4} y^{4}}$ 
C)  $\frac{\sqrt{19}}{x^{4} y^{4}}$ 
D)  $\frac{\sqrt{19}}{x y}$

Question 20

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.
-$\sqrt{(3 y+5)^{2}}$

Accepted Answer

A)  $\sqrt{3 y}+\sqrt{|5|}$ 
B)  $3 y+5$ 
C)  $9 y^{2}+30 y+25$ 
D)  $\sqrt{3 y}-\sqrt{|5|}$ 
A)  $\sqrt{3 y}+\sqrt{|5|}$ 
B)  $3 y+5$ 
C)  $9 y^{2}+30 y+25$ 
D)  $\sqrt{3 y}-\sqrt{|5|}$

Simplify by factoring. - $\sqrt{\mathrm{x}^{6}}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{5 x} \sqrt{15 x}$

Simplify by factoring. - $-\sqrt{432}$

Decide whether or not the radical expression represents a real number. - $\sqrt{16}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{25 x^{2}+30 x+9}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $4 \sqrt{5}+\frac{-2}{\sqrt{5}}$

Provide an appropriate response. -Why must you know how to add and subtract radical expressions before you can rationalize denominators with two terms?

Perform the indicated operation. - $6 \sqrt{5}(\sqrt{11}+\sqrt{5})$

Provide an appropriate response. -Is $\sqrt{11}$ simplified?

Simplify by factoring. - $\sqrt{75 x^{2}}$

Solve the equation. - $\sqrt{2 \mathrm{x}+3}-\sqrt{\mathrm{x}+1}=1$

Solve the equation. - $\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

Divide and simplify. - $\frac{\sqrt{20}}{\sqrt{5}}$

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

Simplify. - $\sqrt{\frac{100}{49}}$

Simplify by factoring. - $\sqrt{486 y^{2}}$

Provide an appropriate response. -If $\mathrm{p}$ is a prime number, is $\sqrt{\mathrm{p}}$ in simplified form? Explain.

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. - $a=30, c=50$

Simplify. - $\sqrt{\frac{19}{\mathrm{x}^{4} \mathrm{y}^{4}}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{(3 y+5)^{2}}$

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

Simplify by factoring. - x6\sqrt{\mathrm{x}^{6}}x6​

Multiply and then, if possible, simplify by factoring. - 5x15x\sqrt{5 x} \sqrt{15 x}5x​15x​

Simplify by factoring. - −432-\sqrt{432}−432​

Decide whether or not the radical expression represents a real number. - 16\sqrt{16}16​

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - 25x2+30x+9\sqrt{25 x^{2}+30 x+9}25x2+30x+9​

Add or subtract. Simplify by collecting like radical terms, if possible. - 45+−254 \sqrt{5}+\frac{-2}{\sqrt{5}}45​+5​−2​

Provide an appropriate response. -Why must you know how to add and subtract radical expressions before you can rationalize denominators with two terms?

Perform the indicated operation. - 65(11+5)6 \sqrt{5}(\sqrt{11}+\sqrt{5})65​(11​+5​)

Provide an appropriate response. -Is 11\sqrt{11}11​ simplified?

Simplify by factoring. - 75x2\sqrt{75 x^{2}}75x2​

Solve the equation. - 2x+3−x+1=1\sqrt{2 \mathrm{x}+3}-\sqrt{\mathrm{x}+1}=12x+3​−x+1​=1

Solve the equation. - 2x+5−x−2=3\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=32x+5​−x−2​=3

Divide and simplify. - 205\frac{\sqrt{20}}{\sqrt{5}}5​20​​

Rationalize the denominator and simplify. - 7+72+2\frac{\sqrt{7}+7}{\sqrt{2}+2}2​+27​+7​

Simplify. - 10049\sqrt{\frac{100}{49}}49100​​

Simplify by factoring. - 486y2\sqrt{486 y^{2}}486y2​

Provide an appropriate response. -If p\mathrm{p}p is a prime number, is p\sqrt{\mathrm{p}}p​ in simplified form? Explain.

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. - a=30,c=50a=30, c=50a=30,c=50

Simplify. - 19x4y4\sqrt{\frac{19}{\mathrm{x}^{4} \mathrm{y}^{4}}}x4y419​​

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - (3y+5)2\sqrt{(3 y+5)^{2}}(3y+5)2​

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

Simplify by factoring. - $\sqrt{\mathrm{x}^{6}}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{5 x} \sqrt{15 x}$

Simplify by factoring. - $-\sqrt{432}$

Decide whether or not the radical expression represents a real number. - $\sqrt{16}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{25 x^{2}+30 x+9}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $4 \sqrt{5}+\frac{-2}{\sqrt{5}}$

Perform the indicated operation. - $6 \sqrt{5}(\sqrt{11}+\sqrt{5})$

Provide an appropriate response. -Is $\sqrt{11}$ simplified?

Simplify by factoring. - $\sqrt{75 x^{2}}$

Solve the equation. - $\sqrt{2 \mathrm{x}+3}-\sqrt{\mathrm{x}+1}=1$

Solve the equation. - $\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

Divide and simplify. - $\frac{\sqrt{20}}{\sqrt{5}}$

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

Simplify. - $\sqrt{\frac{100}{49}}$

Simplify by factoring. - $\sqrt{486 y^{2}}$

Provide an appropriate response. -If $\mathrm{p}$ is a prime number, is $\sqrt{\mathrm{p}}$ in simplified form? Explain.

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. - $a=30, c=50$

Simplify. - $\sqrt{\frac{19}{\mathrm{x}^{4} \mathrm{y}^{4}}}$

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number. - $\sqrt{(3 y+5)^{2}}$