Powers & Roots of Numbers

Practice Questions

GMAT Quantitative Reasoning › Powers & Roots of Numbers

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1

Let $A\ \textup{and }B$ be positive integers. Is $\sqrt{A^{3} B}$ an integer?

Statement 1: is a perfect square.

Statement 2: is an even integer.

2

Let $A\ \textup{and }B$ be positive integers. Is $\sqrt{A^{3} B}$ an integer?

Statement 1: is a perfect square.

Statement 2: is an even integer.

3

is a real number. Is positive, negative, or zero?

Statement 1:

Statement 2: $\frac{1}{2}x^{3} -1> 0$

4

is a real number. Is positive, negative, or zero?

Statement 1:

Statement 2: $\frac{1}{2}x^{3} -1> 0$

5

Imagine an integer such that the units digit of is greater than 5. What is the units digit of ?

(1) The units digit of is the same as the units digit of $y^{2}$ .

(2) The units digit of is the same as the units digit of $y^{3}$ .

6

Imagine an integer such that the units digit of is greater than 5. What is the units digit of ?

(1) The units digit of is the same as the units digit of $y^{2}$ .

(2) The units digit of is the same as the units digit of $y^{3}$ .

7

is a positive real number. True or false: is a rational number.

Statement 1: $N ^{3}$ is an irrational number.

Statement 2: $N ^{4}$ is an irrational number.

8

is a positive real number. True or false: is a rational number.

Statement 1: $N ^{3}$ is an irrational number.

Statement 2: $N ^{4}$ is an irrational number.

9

Simplify this expression as much as possible:

$\sqrt[3]{16} + \sqrt[3]{128} - \sqrt[3]{54}$

10

Simplify this expression as much as possible:

$\sqrt[3]{16} + \sqrt[3]{128} - \sqrt[3]{54}$

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