Question

Simplify the expression. $$\frac{10 \sqrt{8}}{\sqrt{25}}$$

Short answer

The simplified form of the expression is \(4\sqrt{2}\).

Step-by-step solution

Simplify the Square Roots

First, simplify each of the square roots separately. The square root of 25 is a perfect square, so it simplifies to \(5\). The square root of 8 is not a perfect square, but 8 can be broken down into \(4 * 2\), and since 4 is a perfect square, it can be simplified to 2 under the square root. Thus, \( \sqrt{8} = \sqrt{4 * 2} = 2\sqrt{2} \). So the original equation now looks like this: \( \frac{10 * 2\sqrt{2}}{5} \)

Simplify the Fractions

Next, simplify the fractions. The fraction \( \frac{20\sqrt{2}}{5} \) simplifies to \( 4\sqrt{2} \) because 20 divided by 5 equals 4.

Final Answer

After having simplified the square roots and the fraction, the final answer is \(4\sqrt{2}\).