Question

simplify.
10√125

Explanation:

Step1: Factor 125

We know that \( 125 = 25\times5 \), and \( 25 \) is a perfect square. So we can rewrite \( \sqrt{125} \) as \( \sqrt{25\times5} \).

Step2: Use square - root property

Using the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a = 25\) and \( b = 5\) and \( a\geq0,b\geq0 \)), we have \( \sqrt{25\times5}=\sqrt{25}\times\sqrt{5} \). Since \( \sqrt{25} = 5 \), then \( \sqrt{125}=5\sqrt{5} \).

Step3: Multiply by 10

Now we have the original expression \( 10\sqrt{125} \). Substitute \( \sqrt{125}=5\sqrt{5} \) into it, we get \( 10\times5\sqrt{5} \).

Step4: Calculate the product

Calculate \( 10\times5 = 50 \), so \( 10\sqrt{125}=50\sqrt{5} \).

Answer:

\( 50\sqrt{5} \)