Question

simplify.
$4\sqrt{175}$

Explanation:

Step1: Factor 175

We factor 175 into its prime factors. We know that \(175 = 25\times7\), and \(25 = 5^{2}\). So, \(175=5^{2}\times7\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 5^{2}\) and \(b = 7\)), we have \(\sqrt{175}=\sqrt{5^{2}\times7}=\sqrt{5^{2}}\times\sqrt{7}\). Since \(\sqrt{5^{2}} = 5\), then \(\sqrt{175}=5\sqrt{7}\).

Step3: Multiply by the coefficient

We have the original expression \(4\sqrt{175}\). Substituting the simplified square root, we get \(4\times5\sqrt{7}\).

Step4: Calculate the product

Multiplying 4 and 5, we get \(4\times5 = 20\). So, \(4\sqrt{175}=20\sqrt{7}\).

Answer:

\(20\sqrt{7}\)