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 expressing the fraction in its simplest radical form when you can simplify the expression more easily by doing so. This often occurs when the numerator and denominator share common factors or when one of the radicands is a perfect square, making the overall simplification easier.

The rule that allows the radicands to be divided in this way is the quotient rule for square roots, which states:

\[ \sqrt{a} \div \sqrt{b} = \sqrt{\frac{a}{b}} \]

This rule is valid as long as \( b \) is not equal to zero. By applying this rule, you can first compute the fraction of the radicands, which might lead to a simpler expression to work with before taking the square root.