Master Radicals and Equations: Online Quizzes and Practice

Question 1

Which of the following is a conjugate pair?

Accepted Answer

√2 and -√2

Answer

√3 and √3

Answer

√5 and √5

Answer

√7 and √9

Question 2

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

Accepted Answer

A radical expression can have a negative index.

Answer

Radicals of equal indices can be added and subtracted.

Answer

The product of two radicals is a radical of the product of the radicands.

Answer

The quotient of two radicals is a radical of the quotient of the radicands.

Question 3

Which of the following is the conjugate of √(5) - √(3)?

Accepted Answer

√(5) + √(3)

Answer

√(5) - √(3)

Answer

(√(5) + √(3))^2

Answer

(√(5) - √(3))^2

Question 4

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

Accepted Answer

(√2 + 1)²/(√2 - 1)

Answer

(√2 - 1)²/(√2 + 1)

Answer

(√2 + 1)/(√2 + 1)

Answer

(√2 - 1)/(√2 - 1)

Question 5

Rationalize the denominator of the expression 1 / √3.

Accepted Answer

√3 / 3

Answer

3 / √3

Answer

1 / 3

Answer

3

Question 6

The area of a square is 49 square meters. What is the length of one side of the square?

Accepted Answer

7 meters

Answer

14 meters

Answer

21 meters

Answer

28 meters

Question 7

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

Accepted Answer

23

Answer

-23

Answer

43

Answer

-43

Question 8

Simplify the expression: (√2 + √3)^2

Accepted Answer

5 + 2√6

Answer

5 - 2√6

Answer

4 + 2√6

Answer

4 - 2√6

Question 9

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

Accepted Answer

√a = -a

Answer

√(ab) = √a * √b

Answer

√(a/b) = √a / √b

Answer

√(a^n) = a^(n/2)

Question 10

Simplify the expression: √(8/27x^3y^2)

Accepted Answer

2y/(3x^2)

Answer

2y/(3x)

Answer

(2/3)y/x^2

Answer

(2/3)y/x

Question 11

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

Accepted Answer

√(a + b)² = √a + √b

Answer

√(ab) = √a√b

Answer

√(a²) = a

Answer

√(a/b) = √a/√b

Question 12

Simplify the expression: √(64x²y³z) / √(16xy²z²)

Accepted Answer

4x√y

Answer

8x√y

Answer

2x√y

Answer

16x√y

Question 13

What is the conjugate of the expression 2 + √5?

Accepted Answer

2 - √5

Answer

2 + √5

Answer

2√5

Answer

5 - √2

Question 14

Simplify the expression: (√x - √y)/(√x + √y)

Accepted Answer

x - y

Answer

x + y

Answer

y - x

Answer

x/y

Question 15

Which of the following expressions has the greatest value?

Accepted Answer

2√2

Answer

√2

Answer

3

Answer

√3

Question 16

Rationalize the denominator of the expression: 1/√5

Accepted Answer

√5/5

Answer

√5/10

Answer

5/√5

Answer

10/√5

Question 17

Find the conjugate of the expression: 3 + √2

Accepted Answer

3 - √2

Answer

6

Answer

5 + √2

Answer

9 - 2√2

Question 18

Solve the inequality: √(x + 2) > 3

Accepted Answer

x > 1

Answer

x > -1

Answer

x < -1

Answer

x < 1

Question 19

Find the domain of the function: f(x) = √(x - 4)

Accepted Answer

x ≥ 4

Answer

x < 4

Answer

All real numbers

Answer

x > 4

Question 20

Simplify the radical expression: √72

Accepted Answer

6√2

Answer

12√3

Answer

36

Answer

8√3

Question 21

Simplify the product: (√8)(√3)

Accepted Answer

2√6

Answer

8√3

Answer

2√11

Answer

√24

Question 22

Simplify the expression: √(18x^2) / √2  for x > 0

Accepted Answer

3x

Answer

9x√2

Answer

3x√2

Answer

9x

Question 23

Rationalize the denominator: 5 / (√7 - √2)

Accepted Answer

(5√7 + 5√2) / 5

Answer

(5√7 - 5√2) / 5

Answer

(5√7 - 5√2) / 7

Answer

(5√7 + 5√2) / 7

Question 24

Solve the radical equation: √(x + 3) = 4

Accepted Answer

x = 13

Answer

x = 1

Answer

x = 7

Answer

x = 3

Question 25

Find the solution set for the equation: √(2x - 1) - 3 = 1

Accepted Answer

{9}

Answer

{-3}

Answer

{3, -3}

Answer

No Solution

Question 26

Which of the following is a solution to the equation: √(x - 5) = x - 7?

Accepted Answer

x = 9

Answer

x = 9 and x = 6

Answer

No Solution

Answer

x = 6

Question 27

Find the value of x in the equation: √(4x + 1) + √(x - 2) = 3

Accepted Answer

x = 2

Answer

x = 2 and x = 6

Answer

No Solution

Answer

x = 6

Question 28

The area of a square is 50 square units. Express the length of one side of the square in simplest radical form.

Accepted Answer

5√2 units

Answer

25 units

Answer

10 units

Answer

2√5 units

Question 29

A right triangle has legs of length √12 and √27. Calculate the length of the hypotenuse using the Pythagorean theorem.

Accepted Answer

√39

Answer

9

Answer

3√13

Answer

3√3