Master Radical Expressions: Online Quizzes and Practice

Question 1

Which of the following is equivalent to √(a^2b^4)?

Accepted Answer

|ab^2|

Answer

ab^2

Answer

-|ab^2|

Answer

-ab^2

Question 2

Rationalize the denominator of the expression: 1/√3

Accepted Answer

3/√3

Answer

√3/3

Answer

1/3

Answer

3/1

Question 3

Solve the equation: √(2x + 5) = 5

Accepted Answer

x = 10

Answer

x = 0

Answer

x = 2

Answer

x = 12

Question 4

Add the expressions: √6 + √24

Accepted Answer

3√10

Answer

√30

Answer

2√6

Answer

6√5

Question 5

Divide the expressions: (√27)/(√3)

Accepted Answer

3√3

Answer

3

Answer

√3

Answer

1

Question 6

Solve for x: √x + 2 = 6.

Accepted Answer

4

Answer

8

Answer

16

Answer

32

Question 7

Which of the following is the conjugate of the binomial √3 - √2?

Accepted Answer

√3 + √2

Answer

-√3 - √2

Answer

√6

Answer

-√6

Question 8

Solve the equation √(x + 3) = 5.

Accepted Answer

x = 22

Answer

x = 16

Answer

x = 25

Answer

x = 28

Question 9

Which of the following expressions represents the square root of 12 in its simplest radical form?

Accepted Answer

2√3

Answer

4√3

Answer

6√3

Answer

8√3

Question 10

Which of the following is true about radical equations?

Accepted Answer

They may have no real solutions.

Answer

They always have two real solutions.

Answer

They can be solved using any method.

Answer

They can be solved only using the quadratic formula.

Question 11

Which of the following is not considered a radical expression?

Accepted Answer

3π

Answer

√(16)

Answer

2³

Answer

(125)^(1/3)

Question 12

Simplify the radical expression √(49):

Accepted Answer

7

Answer

-7

Answer

14

Answer

Cannot be simplified

Question 13

What is the conjugate of the expression √(5) - √(3)?

Accepted Answer

√(5) + √(3)

Answer

√(5) - √(3)

Answer

-√(5) + √(3)

Answer

-√(5) - √(3)

Question 14

Simplify the expression (2 + √(3))²:

Accepted Answer

4 + 2√(3) + 3

Answer

4 - 2√(3) + 3

Answer

4 + 2√(3) - 3

Answer

4 - 2√(3) - 3

Question 15

Simplify the radical expression: √(81) - √(49)

Accepted Answer

6

Answer

0

Answer

2

Question 16

Multiply and simplify: (√(2) + √(3)) * (√(2) - √(3))

Accepted Answer

-1

Answer

1

Answer

-2

Question 17

Solve the equation: √(x - 5) = 3

Accepted Answer

x = 14

Answer

x = 8

Question 18

Rationalize the denominator: 1 / √(5)

Accepted Answer

√(5) / 5

Answer

5 / √(5)

Question 19

Identify the expression that is NOT a radical expression:

Accepted Answer

x^2

Answer

√(x)

Answer

∛(y)

Question 20

Simplify the expression: √(a) * √(b) * √(c) to its simplest form.

Accepted Answer

√(abc)

Answer

√(a) + √(b) + √(c)

Answer

√(a + b + c)

Answer

a * b * c

Question 21

Rationalize the denominator of the expression: 1/(√5 - 2)

Accepted Answer

5 + 2√5

Answer

√5 + 2

Answer

√5 - 2

Answer

5 - 2√5

Question 22

Solve for x in the equation √(x + 5) = 3, isolating x as the subject of the formula.

Accepted Answer

x = 6

Answer

x = 4

Answer

x = 8

Answer

x = 10

Question 23

Simplify the expression (2√3 - √7)² by expanding and combining like terms.

Accepted Answer

29

Answer

19

Answer

39

Answer

49

Question 24

Which of the following is NOT a fundamental property of radicals?

Accepted Answer

√(a + b) = √a + √b

Answer

√(ab) = √a√b

Answer

√a² = a

Answer

√(1/a) = 1/√a

Question 25

Combine the radicals to find the sum of √2 and √8 in its simplest radical form.

Accepted Answer

2√10

Answer

√10

Answer

√18

Answer

2√18

Question 26

Which of the following is NOT a property of radicals?

Accepted Answer

√(a²) = |a|

Answer

√(ab) = √a * √b

Answer

√(a/b) = √a / √b

Answer

√(a) * √(a) = a

Question 27

Simplify the expression: (√x + √y)². Express your answer in simplest radical form.

Accepted Answer

x + y + 2√(xy)

Answer

x + y - 2√(xy)

Answer

2x + 2y

Answer

x² + y² + 2xy

Question 28

Which of the following expressions is equivalent to the simplified form of (√3 + 1)²?

Accepted Answer

4 + 2√3

Answer

2 + √3

Answer

3 + 2√3

Answer

4 + √3

Question 29

Identify a rationalizing factor for √5:

Accepted Answer

5√5

Answer

√5

Answer

2√5

Answer

10√5

Question 30

Which of the following numbers is NOT a perfect square?

Accepted Answer

12

Answer

4

Answer

9

Answer

16

Question 31

Evaluate the expression: √(81) - √(16)

Accepted Answer

5

Answer

3

Answer

7

Answer

9

Question 32

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

Accepted Answer

0

Answer

-1

Answer

1

Answer

2

Question 33

What is the domain of the function: f(x) = √(x - 2)?

Accepted Answer

{x | x ≥ 2}

Answer

{x | x ≤ 2}

Answer

{x | x > 2}

Answer

{x | x < 2}

Question 34

Which of the following is equivalent to √(-9)?

Accepted Answer

-3i

Answer

3i

Answer

9i

Answer

-9i

Question 35

Which of the following is the conjugate of the expression √5 - √3?

Accepted Answer

√5 + √3

Answer

√5 - √3

Answer

5 + 3

Answer

5 - 3

Question 36

Expand the expression (2√3 + √5)².

Accepted Answer

16 + 10√15

Answer

4 + 10√15

Answer

4 + 2√15

Answer

16 + 2√15

Question 37

Simplify the expression (√2 - √3)/(√2 + √3).

Accepted Answer

-√5

Answer

-1

Answer

1

Answer

√5

Question 38

Which of the following is an example of a rational exponent for a radical expression?

Accepted Answer

1/2

Answer

√2

Answer

π

Answer

i

Question 39

Simplify the expression ∛(216x⁶y⁴).

Accepted Answer

12x²y²

Answer

6x²y²

Answer

18x²y²

Answer

36x²y²

Question 40

Determine the domain of the function y = √(x + 3).

Accepted Answer

x ≥ -3

Answer

x ≤ -3

Answer

x > 0

Answer

All real numbers

Question 41

Which of the following is NOT considered a radical expression?

Accepted Answer

x^2

Answer

√9

Answer

∛64

Answer

√(16 + 9)

Question 42

Determine the conjugate of the radical expression: √5 - √2

Accepted Answer

√5 + √2

Answer

√5 - √2

Answer

√5 * √2

Answer

√5 / √2

Question 43

Divide the radical expressions: √24 / √6

Accepted Answer

2√3

Answer

√4

Answer

4

Answer

2

Question 44

Which of the following is NOT true about radical expressions?

Accepted Answer

They are always positive.

Answer

They can be simplified using radical rules.

Answer

They can be multiplied and divided.

Answer

They can be added and subtracted.

Question 45

Solve the inequality: √(x+2) > 3

Accepted Answer

x > 5

Answer

x < 5

Answer

x > 7

Answer

x < 7

Question 46

Evaluate the value of the expression: √(25) + √(81)

Accepted Answer

10 + 9

Answer

5 + 9

Answer

10 - 9

Answer

13

Question 47

Combine the like radicals: 2√(3) + 5√(3) - √(3)

Accepted Answer

6√(3)

Answer

8√(3)

Answer

4√(3)

Answer

2√(3)

Question 48

Rationalize the denominator of the fraction: 1 / √(5)

Accepted Answer

√(5) / 5

Answer

5 / √(5)

Answer

√(5)

Answer

5

Question 49

Rationalize the numerator of the expression: (√(5) - 1) / (√(5) + 1)

Accepted Answer

(√(5) + 1) / 4

Answer

(√(5) - 1) / 4

Answer

(5 - 1) / 4

Answer

(5 + 1) / 4

Question 50

In simplest form, √8 is equivalent to what?

Accepted Answer

2√2

Answer

2

Answer

4

Answer

8

Question 51

Simplify the radical expression: √(100x^6)

Accepted Answer

10x

Answer

10x^2

Answer

10x^3

Answer

10x^6

Question 52

Perform the division of radical expressions: √54 / √6

Accepted Answer

3√3

Answer

3

Answer

9

Answer

9√3

Question 53

Find the product of the following expression: (√2 - √3)(√2 + √3)

Accepted Answer

1

Answer

-1

Answer

5

Answer

-5

Question 54

Find the domain of the function: y = √(x - 2)

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x < 2

Answer

x > 2