Question

simplify.
$10\sqrt{125}$

Explanation:

Step1: Factor 125 into perfect square and other

We know that \(125 = 25\times5\), where 25 is a perfect square (\(25 = 5^2\)). So we can rewrite \(\sqrt{125}\) as \(\sqrt{25\times5}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we have \(\sqrt{25\times5}=\sqrt{25}\times\sqrt{5}\). Since \(\sqrt{25} = 5\), then \(\sqrt{25}\times\sqrt{5}=5\sqrt{5}\).

Step3: Multiply with the coefficient outside the square - root

We have \(10\sqrt{125}=10\times5\sqrt{5}\).

Step4: Calculate the product of the coefficients

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

Answer:

\(50\sqrt{5}\)