Master Radicals: Conquer Roots and Radicals in College Algebra

Question 1

Simplify √(x^6y^4z^2). What is the simplified form?

Accepted Answer

x^3y^2z

Answer

x^2y^2|z|

Answer

x^4y^2z

Answer

x^3y^2|z|

Question 2

Rationalize the denominator of 1/(√3 + √2). What is the rationalized denominator?

Accepted Answer

3 + 2√6

Answer

√3 - √2

Answer

√3 + √2

Answer

3 - 2√6

Question 3

What is the conjugate of √(x − 3)?

Accepted Answer

√(x + 3)

Answer

−√(x + 3)

Answer

√(x − 3)

Answer

−√(x − 3)

Question 4

If √(x) = 2, what is the value of x^4?

Accepted Answer

256

Answer

4

Answer

16

Answer

64

Question 5

What is a unique characteristic of irrational numbers?

Accepted Answer

They cannot be written as a fraction of two integers.

Answer

They are rational numbers.

Answer

They can be expressed as a terminating or repeating decimal.

Answer

They are always positive.

Question 6

Simplify the radical expression: √(24x³y)

Accepted Answer

2√(6x²y)

Answer

4√(6xy³)

Answer

6√(4x²y)

Answer

8√(3x³y)

Question 7

To rationalize the denominator of 1 / √(5), we should multiply both the numerator and denominator by which of the following?

Accepted Answer

√(5)

Answer

5

Answer

√(25)

Answer

25

Question 8

Which of the following is NOT a property of radicals?

Accepted Answer

√(ab) = √(a) + √(b)

Answer

√(a/b) = √(a) / √(b)

Answer

(√(a))^n = √(a^n)

Answer

(a√(b))^n = a^n√(b^n)

Question 9

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

Accepted Answer

1

Answer

-1

Answer

4

Answer

7

Question 10

To rationalize the denominator of 1 / (√(2) + √(3)), we should multiply both the numerator and denominator by which of the following?

Accepted Answer

√(2) + √(3)

Answer

√(2) - √(3)

Answer

2 - 3

Answer

2 + 3

Question 11

Simplify the expression to 2 + √3:

Accepted Answer

√3(2 + √3)

Answer

2 + √12

Answer

2√3

Answer

6 + √3

Question 12

Simplify: √(16x^4y^2):

Accepted Answer

4x^2y

Answer

4xy^2

Answer

8x^2y

Answer

4|x|^2|y|

Question 13

Evaluate: √(0.04):

Accepted Answer

0.02

Answer

0.2

Answer

0.002

Answer

0.0002

Question 14

Subtract: √32 - √2:

Accepted Answer

2√6

Answer

√6

Answer

2√2

Answer

Cannot be simplified

Question 15

Rationalize the denominator of the expression 1/sqrt(2), by eliminating the radical from the denominator.

Accepted Answer

sqrt(2)/2

Answer

sqrt(2)

Answer

2

Answer

2/sqrt(2)

Question 16

Define a radical expression.

Accepted Answer

An expression that contains any root

Answer

An expression that contains a square root

Answer

An expression that contains a variable

Question 17

If √a = 5, find the value of a.

Accepted Answer

25

Answer

5

Answer

10

Answer

50

Question 18

Multiply the radicals √3 and √5.

Accepted Answer

√15

Answer

5√3

Answer

3√5

Question 19

Which of the following is equivalent to √(25/81)?

Accepted Answer

5/9

Answer

25/9

Answer

81/5

Answer

9/25

Question 20

Which of the following is a property of radicals?

Accepted Answer

√(ab) = √a * √b if a and b are nonnegative.

Answer

√(a²) = a if a is negative.

Answer

√(a + b) = √a + √b.

Answer

√(a - b) = √a - √b if a and b are nonnegative.

Question 21

Simplify the expression: √(32a²b³).

Accepted Answer

4ab√2

Answer

8a²b³

Answer

4a²b³

Answer

16a²b²√2

Question 22

Which of the following is a difference between rational and irrational numbers?

Accepted Answer

Irrational numbers cannot be expressed as a simple fraction, while rational numbers can.

Answer

Irrational numbers are always greater than rational numbers.

Answer

Irrational numbers are negative, while rational numbers are positive.

Question 23

Rationalize the denominator of 1/√3.

Accepted Answer

√3/3

Answer

-√3/3

Answer

3√3

Answer

1/3

Question 24

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

Accepted Answer

14

Answer

11

Answer

-14

Answer

7

Question 25

Which of the following statements about radicals is true?

Accepted Answer

They can represent non-rational numbers.

Answer

They have no practical applications.

Answer

They can only be used to represent square roots.

Answer

They are always positive.

Question 26

Rationalize the denominator of 1 / √5:

Accepted Answer

√5 / 5

Answer

5 / √5

Answer

√5

Answer

1 / 5

Question 27

What is the imaginary unit represented as?

Accepted Answer

√(-1)

Answer

√(-2)

Answer

1

Answer

-1

Question 28

Which property of radicals states that the product of two radicals is equal to the radical of the product of the radicands?

Accepted Answer

√(ab) = √a√b

Answer

√(-a) = √a

Answer

√(a + b) = √a + √b

Answer

√(a/b) = √a / √b

Question 29

Which of the following is the simplified form of √(3)?

Accepted Answer

√3

Answer

3/2

Answer

3

Answer

6

Question 30

What is the result of rationalizing the denominator in 1/(√5)?

Accepted Answer

√5/5

Answer

5/√5

Answer

√5

Answer

5

Question 31

The square root of 121, expressed in radical form, is:

Accepted Answer

11

Answer

11√11

Answer

22

Answer

121

Question 32

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

Accepted Answer

11 + 5√2

Answer

9 - 2√6

Answer

9 + 2√6

Answer

11 - 5√2

Question 33

What is the value of (√3)^-2?

Accepted Answer

1/3

Answer

27

Answer

3

Answer

9

Question 34

Simplify the radical expression: √(16x⁴)

Accepted Answer

4x²

Answer

64x

Answer

8x²

Answer

2x²

Question 35

What is the simplified form of √27?

Accepted Answer

3√3

Answer

3

Answer

√27

Answer

9√3

Question 36

Rationalize the denominator: 3/(√5)

Accepted Answer

3√5 / 5

Answer

3√5

Answer

√15 / 5

Answer

√5 / 3

Question 37

Simplify the expression: (√2 + √3)²

Accepted Answer

5 + 2√6

Answer

5 + √6

Answer

2 + 2√6

Answer

2 + √6

Question 38

What is the simplified form of √(x² + 4x + 4)?

Accepted Answer

x + 2

Answer

x² + 4x + 4

Answer

√(x² + 4x + 4)

Answer

x - 2

Question 39

Which of the following is equivalent to √(1/4)?

Accepted Answer

1/2

Answer

2

Answer

4

Answer

1/4

Question 40

Simplify the radical: √(16x^4y^2)

Accepted Answer

4x²y

Answer

2x²y

Answer

2x³y²

Answer

8x²y

Question 41

Rationalize the denominator of √(3)/√(5):

Accepted Answer

√(3)⋅√(5)/√(15)

Answer

√(3)/√(5⋅15)

Answer

√(3)⋅√(5)/5

Answer

3⋅√(5)/√(5)

Question 42

Find the conjugate of √(2)+√(3):

Accepted Answer

√(2)-√(3)

Answer

√(2)²+√(3)²

Answer

2√(2)+3√(3)

Answer

√(2)+√(3)

Question 43

Add: (√(5)+2√(2))+(√(5)-2√(2))

Accepted Answer

2√(5)

Answer

0

Answer

√(10)

Answer

4

Question 44

Multiply: (2√(3))⋅(5√(6))

Accepted Answer

10√(18)

Answer

10√(9)

Answer

30

Answer

30√(18)

Question 45

Simplify: (√(27x³y²))³

Accepted Answer

27xy³

Answer

9x³y²

Answer

81x³y²

Answer

3x³y²

Question 46

Which of the following is equivalent to √(125/16):

Accepted Answer

5/4

Answer

4

Answer

5

Answer

125/16

Question 47

Solve for x: √(x-2)=5

Accepted Answer

27

Answer

32

Answer

12

Answer

17

Question 48

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

Accepted Answer

x≥4

Answer

x≤4

Answer

x>4

Answer

x∈R

Question 49

Which of the following is the graph of y=√(x+3)-2:

Accepted Answer

//image link to the correct graph//

Answer

//image link to another incorrect graph//

Answer

//image link to an incorrect graph//

Answer

//image link to another incorrect graph//