Section 31-2 Roots Review Solutions and Explanations

Begin by isolating the number under the square root sign. To simplify expressions, try factoring the number into perfect squares. This approach makes it easier to simplify the root and find the correct answer.

When dealing with square roots, always check if the number is a perfect square. If it is, the square root will be a whole number. If not, estimate the value by identifying two perfect squares it lies between, then refine your estimate by trial and error.

In problems involving radicals, remember that simplifying fractions with square roots is crucial. When the numerator or denominator contains a root, simplify them separately, then combine them. Ensure that your final answer is in its simplest form.

Practice working with both positive and negative roots, as some problems may require considering both possibilities. The square root of a negative number involves imaginary numbers, so always pay attention to the signs in your calculations.