Graduate Management Admission Test (GMAT) Practice Test

What is the formula for the square root of the quotient of two numbers a and b?

1. (√a) / (√b)

2. √(a + b)

3. √a + b

4. √(a - b)

The correct answer is: (√a) / (√b)

The formula for the square root of the quotient of two numbers \( a \) and \( b \) is indeed \( \frac{\sqrt{a}}{\sqrt{b}} \). This relationship stems from a fundamental property of square roots known as the quotient rule, which states that the square root of a fraction can be expressed as the square root of the numerator divided by the square root of the denominator. In mathematical terms, if you have \( \sqrt{\frac{a}{b}} \), it can be rewritten as \( \frac{\sqrt{a}}{\sqrt{b}} \). This means that if you are looking to find the square root of the result obtained from dividing \( a \) by \( b \), you can separately find the square roots of \( a \) and \( b \) and then divide those results. The other options do not align with this rule. For instance, the square root of \( a + b \) or \( a - b \) does not yield the same outcome as dividing the square roots of \( a \) and \( b \). Thus, the choice that correctly represents the square root of the quotient is the one that involves the quotient rule, affirming that the answer is