Find each square root. See Example 1. -√144⁄121

Verified step by step guidance

1. Identify the expression to simplify: \(-\sqrt{\frac{144}{121}}\).
2. Recall that the square root of a fraction can be written as the fraction of the square roots: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\).
3. Apply this property to the expression: \(-\sqrt{\frac{144}{121}} = -\frac{\sqrt{144}}{\sqrt{121}}\).
4. Calculate the square roots of the numerator and denominator separately: \(\sqrt{144}\) and \(\sqrt{121}\).
5. Write the simplified expression as \(-\frac{\sqrt{144}}{\sqrt{121}}\) using the values found in the previous step.

Key Concepts

Square Roots of Fractions

The square root of a fraction is found by taking the square root of the numerator and the denominator separately. For example, √(a/b) = √a / √b, provided both a and b are non-negative. This property simplifies the process of finding roots of rational numbers.

Simplifying Square Roots of Perfect Squares

When the numerator and denominator are perfect squares, their square roots are integers. For instance, √144 = 12 and √121 = 11. Recognizing perfect squares allows for straightforward simplification of square roots in fractions.

Handling Negative Signs with Square Roots

A negative sign outside the square root indicates the negative of the root value. For example, -√(144/121) means take the positive square root first, then apply the negative sign. This distinction is important to correctly interpret the expression's value.