Master Radical Expressions: Conquer Radicals in Mathematics

Question 1

Simplify the radical expression: √125

Accepted Answer

5√5

Answer

25

Answer

125

Question 2

Simplify the radical expression: √(16a^4b^6)

Accepted Answer

4a^2b^3

Answer

8a^2b^3

Answer

4a^3b^2

Answer

8a^3b^2

Question 3

Simplify the expression: √(9x^2y^3)

Accepted Answer

3xy√3

Answer

9xy√3

Answer

3x√9y

Answer

9x√9y

Question 4

Simplify the expression: (x^2 * x^1/2)^(1/2)

Accepted Answer

x^(3/4)

Answer

x^(5/4)

Answer

x^(1/2)

Answer

x^(1/4)

Question 5

Simplify the radical expression: √(16y^2)

Accepted Answer

4y

Answer

8y

Answer

16y

Answer

y

Question 6

Rationalize the denominator of the expression: √(3)/√(7)

Accepted Answer

√(21)/7

Answer

3√(21)/7

Answer

√(21)/3

Answer

3√(7)

Question 7

Multiply the radical expressions: √(2) * √(6)

Accepted Answer

2√(3)

Answer

√(12)

Answer

√(3)

Answer

3√(2)

Question 8

Find the smallest positive value of x that satisfies the inequality: √(x - 2) < 3

Accepted Answer

x = 7

Answer

x = 5

Answer

x = 9

Answer

x = 11

Question 9

Divide the radical expressions: √24 / √6

Accepted Answer

2

Answer

4

Answer

6

Answer

√4

Question 10

Solve the radical equation: √x = 5

Accepted Answer

5

Answer

10

Answer

25

Answer

50

Question 11

Which of the following is equivalent to the expression: 2√3 - √27?

Accepted Answer

√18 - √27

Answer

-√18 - √27

Answer

√18 + √27

Answer

2√3 + √27

Question 12

Which of the following is the greatest value?

Accepted Answer

4√4

Answer

√10

Answer

2√2

Answer

3√3

Question 13

Add the following radical expressions: √5 + √20:

Accepted Answer

5√5

Answer

3√5

Answer

√25

Answer

Cannot be simplified further

Question 14

Divide the following radical expressions: √27 / √3:

Accepted Answer

3

Answer

√9

Answer

9

Answer

Cannot be simplified further

Question 15

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

Accepted Answer

x^4

Answer

x^8

Answer

x^2

Answer

Cannot be simplified further

Question 16

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

Accepted Answer

5√5

Answer

√5

Answer

1/√5

Answer

5

Question 17

Multiply the radical expressions: √5 ⋅ √10

Accepted Answer

10√5

Answer

√50

Answer

5√2

Answer

2√10

Question 18

Divide the radical expressions: √72 ÷ √8

Accepted Answer

3√6

Answer

3√2

Answer

6√3

Answer

2√6

Question 19

Rationalize the denominator of the expression: 1 / √5

Accepted Answer

√5 / 5

Answer

5 / √5

Answer

1 / 5√5

Answer

5√5 / 5

Question 20

Which of the following is the conjugate of the radical expression √2 - √3?

Accepted Answer

√2 + √3

Answer

√2 - √3

Answer

2 + 3

Answer

2 - 3

Question 21

Divide the radical expressions: (6√(5)) / (2√(5))

Accepted Answer

3

Answer

3√(5)

Answer

√(5)

Answer

5√(3)

Question 22

Simplify the radical expression: (√(2) + √(3))^2

Accepted Answer

5 + 2√(6)

Answer

5 - 2√(6)

Answer

2 + 2√(6)

Answer

2 - 2√(6)

Question 23

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

Accepted Answer

(√(5) - √(2)) / 3

Answer

(√(5) + √(2)) / 3

Answer

(√(5) - √(2)) / 5

Answer

(√(5) + √(2)) / 5

Question 24

Solve the equation: √(x + 5) = 3

Accepted Answer

x = 4

Answer

x = 2

Answer

x = -2

Answer

x = -4

Question 25

Add the cube root expressions: ∛(8) + ∛(125)

Accepted Answer

5 + 5∛(5)

Answer

5 - 5∛(5)

Answer

5 + 5√(5)

Answer

5 - 5√(5)

Question 26

Find the value of x such that √(x + 5) = 5.

Accepted Answer

25

Answer

10

Answer

20

Answer

30

Question 27

Which of the following is equivalent to √(a^2b^3)?

Accepted Answer

ab√b

Answer

a√ab

Answer

ab^2√b

Answer

a^2b√b

Question 28

Solve the following inequality: √(x - 7) > 3.

Accepted Answer

x > 22

Answer

x > 16

Answer

x > 10

Answer

x > 4

Question 29

Divide the expressions √27 and √3.

Accepted Answer

3

Answer

1

Answer

√9

Answer

9

Question 30

Solve the equation: √(x - 5) = 3

Accepted Answer

14

Answer

9

Answer

4

Answer

1

Question 31

Find the quotient: √(18) ÷ √(2)

Accepted Answer

3

Answer

12

Answer

9

Answer

6

Question 32

Solve the equation: 2√(x) = 10

Accepted Answer

25

Answer

50

Answer

10

Question 33

Find the value of √(-64)

Accepted Answer

8i

Answer

8

Answer

16i

Answer

-8

Question 34

Express the radical expression √(12x³y⁴z²) in its simplified form

Accepted Answer

2x³/²y²z√(3xy)

Answer

6x³y⁴z²

Answer

2x²y³z²√(x)

Answer

4x³y⁴z²

Question 35

Expand and simplify: (√(3) + √(5))²

Accepted Answer

8 + 2√(15)

Answer

16

Answer

2√(15)

Answer

8 - 2√(15)

Question 36

Add the radical expressions: 2√(5) + √(5)

Accepted Answer

3√(5)

Answer

5√(5)

Answer

5√(2)

Answer

√(10)

Question 37

Divide the radical expressions: √(27) / √(3)

Accepted Answer

3

Answer

√(9)

Answer

√(81)

Question 38

Solve the equation: √(x + 3) = 5

Accepted Answer

22

Answer

17

Answer

28

Answer

8

Question 39

Divide the radical expressions: (12√10)/(2√5)

Accepted Answer

6√2

Answer

2√10

Answer

6/√10

Answer

4√5

Question 40

Solve for x: √(x + 5) = 4

Accepted Answer

11

Answer

5

Answer

9

Answer

15

Question 41

Simplify the radical expression: √72

Accepted Answer

6√2

Answer

2√36

Answer

9√8

Answer

36√2

Question 42

Simplify: (√5 + √2)(√5 - √2)

Accepted Answer

3

Answer

5 - √2

Answer

√7

Answer

√25 + √4

Question 43

Simplify: (√18)/(√2)

Accepted Answer

3

Answer

√36

Answer

√9

Answer

√16

Question 44

Which of the following is equivalent to ∛8x³?

Accepted Answer

2x

Answer

2x³

Answer

8x

Question 45

Simplify the expression: 2√12 - √75

Accepted Answer

√3

Answer

√63

Answer

√-33

Answer

4√3 - 5√3

Question 46

What is the value of (√2)²?

Accepted Answer

2

Answer

4

Answer

√4

Answer

√2

Question 47

Simplify: (√x)³

Accepted Answer

x√x

Answer

x³

Answer

√x³

Question 48

Which of the following expressions is NOT equivalent to √16?

Accepted Answer

√8 + √8

Answer

4

Answer

2√4

Answer

√(4²)