Question

simplify
$3\sqrt{175}$

Explanation:

Step1: Factor 175

We know that \(175 = 25\times7\), where 25 is a perfect square. So, \(\sqrt{175}=\sqrt{25\times7}\).

Step2: Use square - root property

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{25\times7}=\sqrt{25}\times\sqrt{7}\). Since \(\sqrt{25} = 5\), then \(\sqrt{175}=5\sqrt{7}\).

Step3: Multiply by the coefficient

We have \(3\sqrt{175}\), substitute \(\sqrt{175}=5\sqrt{7}\) into it, we get \(3\times5\sqrt{7}\).

Step4: Calculate the product

\(3\times5 = 15\), so \(3\sqrt{175}=15\sqrt{7}\).

Answer:

\(15\sqrt{7}\)