When dividing square roots, when is it beneficial to divide the radicands before expressing the fraction in its simplest radical form? What rule allows the radicands to be divided in this way?(2 points)

Answer 1

When dividing square roots, it is beneficial to divide the radicands before simplifying the fraction when both the numerator and the denominator are perfect squares or when the radicands can be simplified. This can simplify the square root calculation, making it easier to express the result in its simplest radical form.

The rule that allows for this division of radicands is known as the quotient rule for square roots, which states:

\[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \quad \text{(for } b \neq 0\text{)} \]

This rule enables you to take the square root of the numerator and denominator separately after dividing the radicands, leading to a potentially simpler calculation.