HW: Rationalizing the Denominator (Algebra 2)

Match each of the following to its correct simplified form.

Simplify

Answer explanation

To simplify, we can factor out the common terms. The expression simplifies to 2√2, which is the correct choice among the options provided.

Tags

CCSS.HSN.RN.A.2

Which of the following is a perfect square?

• 132

• 90

• 40

• 64

• 625

Answer explanation

A perfect square is an integer that is the square of another integer. Among the choices, 64 (8x8) and 625 (25x25) are perfect squares. 132 and 90 are not perfect squares.

Tags

CCSS.8.EE.A.2

Which of the following in NOT a perfect square?

• 42

• 81

• 111

• 144

• 1000

Answer explanation

A perfect square is an integer that is the square of another integer. Among the choices, 81 (9x9), 144 (12x12), and 100 (10x10) are perfect squares. 42, 111, and 1000 are not perfect squares.

Tags

CCSS.8.EE.A.2

Simplify the following radical: √32

• 3√2

• 4√8

• 16√2

• 4√2

Answer explanation

To simplify √32, we can factor it as √(16*2). Since √16 = 4, we have √32 = 4√2. Thus, the correct answer is 4√2.

• 17√2
• 9√1
• 9
• 9√2

• -5√1
• 8√2 + 13√3
• 21√5
• 20√5

• 13√3
• 10√30
• 13√6
• 11√3

Answer explanation

To simplify \( \frac{2}{\sqrt{3}} \), multiply the numerator and denominator by \( \sqrt{3} \) to get \( \frac{2\sqrt{3}}{3} \). This matches the correct answer choice \( \frac{2\sqrt{3}}{3} \).

• 1

Answer explanation

To simplify \( \frac{1}{\sqrt{7}} \), multiply the numerator and denominator by \( \sqrt{7} \) to get \( \frac{\sqrt{7}}{7} \). Thus, the correct answer is \( \frac{\sqrt{7}}{7} \).