Master Radical Expressions: Conquer Radicals with Confidence

Question 1

Find the value of √(9) - √(4)

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 2

Which of the following is equivalent to the square root of 8?

Accepted Answer

2 multiplied by the square root of 2

Answer

4

Answer

8

Answer

16

Question 3

What is the result of squaring the square root of 5?

Accepted Answer

25

Answer

5

Answer

10

Answer

50

Question 4

Which of the following is a rational number?

Accepted Answer

The square root of one-fourth

Answer

The square root of 2

Answer

The square root of three-halves

Answer

The square root of pi

Question 5

What is the domain of the function f(x) equals the square root of x plus 2?

Accepted Answer

x is greater than or equal to -2

Answer

x is less than or equal to -2

Answer

x is greater than 0

Answer

All real numbers

Question 6

Evaluate the expression: √(4) + √(9)

Accepted Answer

13

Answer

5

Answer

9

Answer

25

Question 7

Simplify the expression: √(27x^3y^2) / √(3x)

Accepted Answer

3x^2y^2

Answer

9x^2y^2

Answer

3x^2y

Answer

9x^2y

Question 8

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 9

Solve the equation: √(x^2-4) = 5

Accepted Answer

x = 3 or x = -3

Answer

x = 9

Answer

x = 25

Answer

No solution

Question 10

Find the solution to the equation: √(x+5) = 5

Accepted Answer

5

Answer

0

Answer

10

Answer

25

Question 11

Find the length of a side of a square with an area of 16 square inches.

Accepted Answer

4 inches

Answer

2 inches

Answer

8 inches

Answer

16 inches

Question 12

Which of the following expressions is irrational?

Accepted Answer

√5

Answer

√4

Answer

√(1/4)

Answer

2

Question 13

Find the expression that is not a perfect cube.

Accepted Answer

8

Answer

64

Answer

125

Answer

27

Question 14

Identify the pair of conjugate radicals:

Accepted Answer

√2 and -√2

Answer

√2 and √3

Answer

√2 and 2√2

Answer

√2 and 2

Question 15

Find the least possible value of the expression √(x²) for all real numbers x:

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 16

Evaluate the expression: √(8) - 2√(2).

Accepted Answer

2√(2)

Answer

0

Answer

2

Answer

-2√(2)

Question 17

Simplify the expression: (2√(3))(3√(5)).

Accepted Answer

6√(15)

Answer

√(15)

Answer

2√(15)

Answer

6√(5)

Question 18

Find the rationalized denominator for the expression: 1 / √(5).

Accepted Answer

√(5) / 5

Answer

√(5)

Answer

5

Answer

1 / √(5)

Question 19

Simplify the expression: √(12x²y³z) / √(3xz³).

Accepted Answer

2xy√(3xz)

Answer

2xy√(3z)

Answer

2y√(3xz)

Answer

2x√(3yz)

Question 20

Which of the following is an irrational number?

Accepted Answer

π

Answer

√(9)

Answer

0.5

Answer

10

Question 21

Simplify the expression: (√(5) + √(2))².

Accepted Answer

7 + 2√(10)

Answer

5 + 2√(10)

Answer

5 - 2√(10)

Answer

7 - 2√(10)

Question 22

Identify the conjugate of the radical expression √7.

Accepted Answer

-√7

Answer

√7

Answer

7

Question 23

Identify the conjugate of the radical expression √(3+√5).

Accepted Answer

√(3-√5)

Answer

√(3+√5)

Answer

(3-√5)

Answer

(3+√5)

Question 24

Simplify the expression √(64) - √(16) to the correct result.

Accepted Answer

4

Answer

0

Answer

8

Answer

16

Question 25

Which of the following expressions is equivalent to the square root of 12?

Accepted Answer

2 multiplied by the square root of 3

Answer

3

Answer

6

Answer

4 multiplied by the square root of 3

Question 26

Which of the following is NOT a rule for radicals?

Accepted Answer

The square root of negative a is the same as negative the square root of a

Answer

The square root of a multiplied by b is the same as the square root of a multiplied by the square root of b

Answer

The square root of a divided by b is the same as the square root of a divided by the square root of b

Answer

The square root of a squared is equal to a

Question 27

Which of the expressions represents the conjugate of the square root of x minus 3?

Accepted Answer

The square root of x plus 3

Answer

The square root of x minus 3

Answer

x plus 3

Answer

x minus 3

Question 28

Simplify the expression: ((x to the power of 3/2) divided by (y to the power of 1/2)) to the power of 2/3

Accepted Answer

x to the power of 2/3 divided by y to the power of 1/3

Answer

x divided by y to the power of 2/3

Answer

x to the power of 1/2 divided by y to the power of 2/3

Answer

x to the power of 2/3 multiplied by y to the power of 1/3

Question 29

Simplify the expression: √(125)

Accepted Answer

5√5

Answer

5

Answer

10

Answer

10√5

Question 30

Simplify the expression: √(12) - √(3)

Accepted Answer

3√(3)

Answer

√(9)

Answer

3√(4)

Answer

6

Question 31

Which of the following is the conjugate of √2 + √3?

Accepted Answer

√2 - √3

Answer

√2 + √3

Answer

2 - 3

Answer

2 + 3

Question 32

Which of the following is equivalent to √(-9x²)?

Accepted Answer

-3ix

Answer

3ix

Answer

9ix

Answer

-9ix

Question 33

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

Accepted Answer

√(a*b) = √a + √b

Answer

√a * √b = √(a*b)

Answer

√a^2 = |a|

Answer

√(a/b) = √a / √b

Question 34

Simplify the expression: (√3)^4

Accepted Answer

81

Answer

9

Answer

27

Question 35

What is the simplified form of √72?

Accepted Answer

6√2

Answer

36√2

Answer

12√3

Answer

2√18

Question 36

What is the domain of the function f(x) = √(x - 4)?

Accepted Answer

x ≥ 4

Answer

All real numbers

Answer

x > 4

Answer

x ≤ 4

Question 37

Which of the following is NOT a step in simplifying the expression (√8 + √18) / √2 ?

Accepted Answer

Square the entire expression to eliminate the radicals.

Answer

Simplify the radicals in the numerator.

Answer

Rationalize the denominator by multiplying by √2 / √2.

Question 38

Simplify the radical expression √(162)

Accepted Answer

9

Answer

18

Answer

24

Answer

6

Question 39

Evaluate the expression √(25) + √(4)

Accepted Answer

9

Answer

5

Answer

21

Answer

16

Question 40

Multiply the radical expressions √(3) * √(12)

Accepted Answer

2√(9)

Answer

3√(4)

Answer

15

Answer

6

Question 41

Rationalize the denominator of the expression 1/√2.

Accepted Answer

√2/2

Answer

2

Answer

2/√2

Answer

1/2

Question 42

Solve the radical equation √(x + 5) = 3

Accepted Answer

4

Answer

-4

Answer

9

Answer

16

Question 43

Which of the following is equivalent to √(8x³y²)?

Accepted Answer

2x√(2xy)

Answer

4x³y

Answer

2x²y√(2)

Answer

8x²y

Question 44

Simplify the expression (√(3) + √(5))².

Accepted Answer

8 + 2√(15)

Answer

16 + 2√(15)

Answer

6 + 2√(15)

Answer

8 - 2√(15)

Question 45

Which of the following is NOT a property of radical expressions?

Accepted Answer

√(a) + √(b) = √(a + b)

Answer

√(a²/b²) = a/b

Answer

√(ab) = √(a) * √(b)

Answer

(√(a))² = a

Question 46

The side length of a square is given by the expression 2√(3) inches. What is the area of the square?

Accepted Answer

12 square inches

Answer

18 square inches

Answer

6 square inches

Answer

24 square inches