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

Verified step by step guidance

1. Identify the expression: $-\sqrt{\frac{144}{121}}$.
2. Recognize 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: $-\frac{\sqrt{144}}{\sqrt{121}}$.
3. Calculate the square root of the numerator: $\sqrt{144}=12$.
4. Calculate the square root of the denominator: $\sqrt{121}=11$.
5. Combine the results to express the square root of the fraction: $-\frac{12}{11}$.

Key Concepts

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 144 is 12, since 12 × 12 = 144. Square roots can be positive or negative, but by convention, the principal square root is the non-negative one.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In the expression -√144/121, both 144 and 121 are perfect squares, and their square roots (12 and 11, respectively) are rational numbers, allowing for straightforward simplification.

Simplifying Radicals

Simplifying radicals involves reducing a square root expression to its simplest form. This includes factoring out perfect squares from under the radical sign. In the case of -√144/121, simplifying involves calculating the square roots of the numerator and denominator separately, leading to a clearer and more manageable expression.