Question

simplify.
$4\sqrt{175}$

Explanation:

Step1: Factor 175 into perfect square and other

We know that \(175 = 25\times7\), where \(25\) is a perfect square (\(25 = 5^{2}\)). So we can rewrite \(\sqrt{175}\) as \(\sqrt{25\times7}\).

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 \(\sqrt{25\times7}=\sqrt{25}\times\sqrt{7}\). Since \(\sqrt{25} = 5\), then \(\sqrt{25\times7}=5\sqrt{7}\).

Step3: Multiply by the coefficient outside the square - root

We have \(4\sqrt{175}=4\times\sqrt{175}\), and since \(\sqrt{175} = 5\sqrt{7}\), then \(4\times\sqrt{175}=4\times5\sqrt{7}\).

Step4: Calculate the product of the coefficients

Calculate \(4\times5 = 20\), so \(4\times5\sqrt{7}=20\sqrt{7}\).

Answer:

\(20\sqrt{7}\)