Free practice questions/GMAT Focus Edition
GMAT Focus Edition — Exponents & Roots
6 free practice questions with full explanations.
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Start freeQuestion 1
What is the value of 8^(2/3)?
- A) 2
- B) 4
- C) 8
- D) 16
Show answer & explanation
Correct answer: B) 4
8^(2/3) = (8^(1/3))^2 = 2^2 = 4.
Question 2
Simplify: (2^5)(2^3) / 2^4
- A) 2^2
- B) 2^3
- C) 2^4
- D) 2^6
Show answer & explanation
Correct answer: C) 2^4
Using exponent rules: (2^5)(2^3) = 2^8. Then 2^8 / 2^4 = 2^(8-4) = 2^4.
Question 3
What is the value of the square root of 144 plus the square root of 81?
- A) 19
- B) 20
- C) 21
- D) 22
Show answer & explanation
Correct answer: C) 21
sqrt(144) = 12 and sqrt(81) = 9. 12 + 9 = 21.
Question 4
If x^3 = 27 and y^2 = 49, what is the value of x + y (assuming x and y are positive)?
- A) 8
- B) 9
- C) 10
- D) 11
Show answer & explanation
Correct answer: C) 10
x^3 = 27 means x = 3. y^2 = 49 means y = 7 (taking the positive root). x + y = 3 + 7 = 10.
Question 5
Simplify: 5^(-2)
- A) -25
- B) -10
- C) 1/10
- D) 1/25
Show answer & explanation
Correct answer: D) 1/25
A negative exponent means take the reciprocal: 5^(-2) = 1/5^2 = 1/25.
Question 6
Simplify: sqrt(50) + sqrt(18)
- A) 8 sqrt(2)
- B) 6 sqrt(2)
- C) 68
- D) sqrt(68)
Show answer & explanation
Correct answer: A) 8 sqrt(2)
sqrt(50) = sqrt(25x2) = 5 sqrt(2). sqrt(18) = sqrt(9x2) = 3 sqrt(2). Sum = 5sqrt(2) + 3sqrt(2) = 8 sqrt(2).
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