Find each square root. See Example 1. √4⁄25

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Identify the expression under the square root: \(\sqrt{\frac{4}{25}}\).

Recall the property of square roots for fractions: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) where \(a\) and \(b\) are positive numbers.

Apply this property to rewrite the expression as \(\frac{\sqrt{4}}{\sqrt{25}}\).

Find the square root of the numerator: \(\sqrt{4}\), and the square root of the denominator: \(\sqrt{25}\).

Express the simplified fraction as \(\frac{\sqrt{4}}{\sqrt{25}}\) with the square roots replaced by their simplified values.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Square Root of a Fraction

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 simplifies the process of finding roots of rational numbers.

Simplifying Square Roots

Simplifying square roots involves expressing the radicand as a product of perfect squares and other factors. This helps in reducing the square root to its simplest form, making calculations easier and results clearer.

Properties of Square Roots

Square roots have properties such as √(x²) = |x| and √(xy) = √x × √y. Understanding these properties allows for manipulation and simplification of expressions involving roots, which is essential for solving root-related problems.

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