DSQ: Understanding powers and roots

Practice Questions

GMAT Quantitative Reasoning › DSQ: Understanding powers and roots

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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

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

Statement 1:

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

3

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 $y^{3}$ .

4

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.

5

Simplify this expression as much as possible:

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

6

and are integers. Is $A ^{B}$ positive, negative, or zero?

Statement 1: is negative.

Statement 2: is odd.

7

What is the value of twelve raised to the fourth power?

8

Simplify: $\frac{5}{\sqrt{4a}}$

9

. True or false: is rational.

Statement 1: $\sqrt{N+1}$ is irrational.

Statement 2: $\sqrt{N-1}$ is rational.

10

is a positive real number. True or false: $\sqrt{N}$ is a rational number.

Statement 1: is irrational.

Statement 2: $\sqrt[4]{N}$ is irrational.

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