Question

simplify.
$4\sqrt{275}$

Explanation:

Step1: Factor 275

Factor 275 into prime factors: \(275 = 25\times11\), and \(25 = 5^2\). So \(275 = 5^2\times11\).

Step2: Simplify the square root

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{275}=\sqrt{5^2\times11}=\sqrt{5^2}\times\sqrt{11}=5\sqrt{11}\).

Step3: Multiply by 4

Now, multiply by 4: \(4\sqrt{275}=4\times5\sqrt{11}=20\sqrt{11}\).

Answer:

\(20\sqrt{11}\)