Algebra Test Exponents and Radicals 2 — Questions and Answers
Question 1: Simplify: √50
- 5
- 5√2 (Correct answer)
- 10√2
- 25√2
Correct answer: 5√2
√50 = √(25 × 2) = √25 · √2 = 5√2.
Question 2: What is 4^(1/2)?
Correct answer: 2
4^(1/2) equals √4 = 2, since 2² = 4.
Question 3: Simplify: √(x⁴), assuming x ≥ 0
Correct answer: x²
√(x⁴) = x^(4/2) = x².
Question 4: Which expression is equivalent to ∛(x⁶)?
- x² (Correct answer)
- x³
- x⁹
- x¹⁸
Correct answer: x²
∛(x⁶) = x^(6/3) = x².
Question 5: Simplify: (2x²)³
- 2x⁵
- 6x⁶
- 8x⁵
- 8x⁶ (Correct answer)
Correct answer: 8x⁶
Apply the power to each factor: 2³ = 8 and (x²)³ = x⁶, giving 8x⁶.
Question 6: What is √72 in simplified radical form?
- 6√2 (Correct answer)
- 8√3
- 6√3
- 4√6
Correct answer: 6√2
√72 = √(36 × 2) = √36 · √2 = 6√2.
Question 7: What is 27^(1/3)?
Correct answer: 3
27^(1/3) is the cube root of 27; since 3³ = 27, the answer is 3.
