Math Problem Statement

Find the square root of \(\frac{24}{25}\).

Solution

The problem asks to find the square root of the given fraction:

2425\sqrt{\frac{24}{25}}

To solve:

  1. Apply the square root property to a fraction: 2425=2425\sqrt{\frac{24}{25}} = \frac{\sqrt{24}}{\sqrt{25}}

  2. Simplify the denominator: 25=5\sqrt{25} = 5 So, the denominator becomes 5.

  3. Simplify the numerator: The square root of 24 is not a perfect square, but it can be simplified: 24=46=46=26\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6}

  4. Combine results: 2425=265\sqrt{\frac{24}{25}} = \frac{2\sqrt{6}}{5}

Thus, the simplified form of the square root is:

265\boxed{\frac{2\sqrt{6}}{5}}

Would you like me to explain any step in more detail or provide additional practice questions?

Here are 5 related questions for practice:

  1. Simplify 49100\sqrt{\frac{49}{100}}.
  2. Find the square root of 1681\frac{16}{81}.
  3. Simplify 50121\sqrt{\frac{50}{121}}.
  4. Calculate the square root of 1225\frac{12}{25} and write it in simplest form.
  5. Solve 964\sqrt{\frac{9}{64}}.

Tip: Always simplify square roots by factoring into perfect squares for easier calculations!

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Math Problem Analysis

Mathematical Concepts

Simplifying square roots
Square root of fractions
Factorization

Formulas

\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
\(\sqrt{n \cdot m} = \sqrt{n} \cdot \sqrt{m}\)

Theorems

Properties of square roots

Suitable Grade Level

Grades 8-10