Master Radical Expressions and Equations: Interactive Quizzes and Practice

Question 1

Identify the expression that is NOT a perfect square.

Accepted Answer

36

Answer

16

Answer

25

Answer

49

Question 2

Simplify the radical expression: √(12).

Accepted Answer

2√3

Answer

4√3

Answer

6√2

Answer

8√3

Question 3

Rationalize the denominator of the expression: 1/√5.

Accepted Answer

√5/5

Answer

5/√5

Answer

5√5

Answer

√5

Question 4

Solve the radical inequality: x - √5 < 2.

Accepted Answer

x < 7

Answer

x > 7

Answer

x < 2

Answer

x > 2

Question 5

Simplify the expression: √(16x^6).

Accepted Answer

8x^3

Answer

4x^3

Answer

8x^2

Answer

4x^6

Question 6

Which expression is equivalent to √(x²)?

Accepted Answer

|x|

Answer

x

Answer

-x

Answer

±x

Question 7

Rationalize the numerator: √2/(√2 - 1)

Accepted Answer

2 + √2

Answer

2 - √2

Answer

√2 + 1

Answer

√2 - 1

Question 8

Simplify: (√5 + √3)²

Accepted Answer

8 + 2√15

Answer

8 - 2√15

Answer

16 + 2√15

Answer

16 - 2√15

Question 9

Which of the following is equivalent to √(-4)√(-9), where i is the imaginary unit?

Accepted Answer

-6i

Answer

3√2

Answer

6i

Answer

-3√2

Question 10

Find the value of x in the equation x² = 32 by taking the square root of both sides.

Accepted Answer

x = ±4√2

Answer

x = ±8

Answer

x = ±16

Answer

x = ±32

Question 11

Which property is used to derive the equation √(a * b) = √a * √b?

Accepted Answer

Product Rule

Answer

Quotient Rule

Answer

Power Rule

Answer

Reciprocal Rule

Question 12

Simplify the expression: (√2 + √3)(√2 - √3)

Accepted Answer

1

Answer

2

Answer

-1

Answer

-2

Question 13

What is the conjugate of √5 - √3?

Accepted Answer

√5 + √3

Answer

√5 - √3

Answer

-√5 - √3

Answer

-√5 + √3

Question 14

Determine the domain and range of the function: f(x) = √(x + 2)

Accepted Answer

Domain: x ≥ -2, Range: y ≥ 0

Answer

Domain: x ≥ 0, Range: y ≥ 2

Answer

Domain: x ≤ -2, Range: y ≤ 0

Answer

Domain: x ≤ 0, Range: y ≤ 2

Question 15

What is the value of (√3)^6?

Accepted Answer

81√3

Answer

3√3

Answer

9√3

Answer

27√3

Question 16

Simplify the radical expression √(24):

Accepted Answer

4√6

Answer

12

Question 17

Solve the radical equation √(x + 2) = 4:

Accepted Answer

x = 16

Answer

x = 14

Question 18

Simplify the expression (√x + 3)(√x - 3):

Accepted Answer

x - 9

Question 19

Which of the following is the conjugate of the expression √2 + √3:

Accepted Answer

√2 - √3

Answer

√2 + √3

Question 20

Simplify the expression √(x^2 + 2x + 1) - x:

Accepted Answer

x

Question 21

Which of the following is the square root of 9 + 12√2:

Accepted Answer

3 + 2√2

Answer

3 - 2√2

Question 22

Rationalize the denominator of the expression: (2/√5)

Accepted Answer

2√5/5

Answer

√5/2

Answer

2/5

Answer

5/2

Question 23

Which of the following statements about √(-16) is correct?

Accepted Answer

It is a non-real number.

Answer

It is a real number.

Answer

It is equal to 0.

Answer

It is undefined.

Question 24

The area of a square is 32 cm^2. What is the length of one side of the square?

Accepted Answer

8 cm

Answer

4 cm

Answer

16 cm

Answer

32 cm

Question 25

Simplify the expression: √(100/81)

Accepted Answer

5/9

Answer

10/9

Answer

5/3

Answer

10/3

Question 26

The volume of a sphere is given by V = (4/3)πr^3, where V is the volume and r is the radius of the sphere. If the volume of a sphere is 288π cm^3, what is the radius of the sphere?

Accepted Answer

9 cm

Answer

6 cm

Answer

12 cm

Answer

18 cm

Question 27

Rationalize the denominator of the expression 1/√5.

Accepted Answer

√5

Answer

5

Answer

1/5

Answer

Cannot be rationalized

Question 28

Rationalize the denominator of $\frac{1}{\sqrt{2}}.$

Accepted Answer

$\frac{\sqrt{2}}{2}$

Answer

$\frac{1}{2}$

Answer

$\frac{2}{\sqrt{2}}$

Question 29

Solve the radical inequality $\sqrt{x-1}<4.$

Accepted Answer

x<17

Answer

x>17

Answer

x>1

Answer

x<1

Question 30

Simplify the following radical expression: √(x^(6) * y^(8))

Accepted Answer

x^(3) * y^(4)

Answer

x^(3) * y^(8)

Answer

x^(6) * y^(4)

Answer

x^(9) * y^(12)

Question 31

Rationalize the denominator of the expression: 3 / √5

Accepted Answer

3√5 / 5

Answer

√5 / 3

Answer

3 / 5

Question 32

Simplify the following expression: √8 / √2

Accepted Answer

2

Answer

√4

Answer

4

Answer

√16

Question 33

Solve the following radical equation: √(x + 2) = 4

Accepted Answer

x = 14

Answer

x = 16

Answer

x = 18

Answer

x = 2

Question 34

Which of the following is a solution to the equation √(2x + 1) = 3?

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 1

Answer

x = 3

Question 35

The area of a square is given by the expression √169. What is the length of one side of the square?

Accepted Answer

13

Answer

13√2

Answer

169

Answer

84.5

Question 36

Simplify the following expression: (√3 + √2)(√3 - √2)

Accepted Answer

1

Answer

√5

Answer

√6

Answer

5

Question 37

The length of a rectangle is √12 and its width is √3. What is the area of the rectangle?

Accepted Answer

6

Answer

√15

Answer

√36

Answer

3√4

Question 38

Solve for x in the following equation: 2√x - 5 = 1

Accepted Answer

x = 9

Answer

x = 4

Answer

x = 3

Answer

x = 1