Question

simplify.
$4\sqrt{28}$

Explanation:

Step1: Factor 28 into perfect square and other factor

We know that \(28 = 4\times7\), where 4 is a perfect square (\(4 = 2^2\)). So we can rewrite \(\sqrt{28}\) as \(\sqrt{4\times7}\).

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

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 4,b = 7\)), we have \(\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}\). Since \(\sqrt{4}=2\), then \(\sqrt{4}\times\sqrt{7} = 2\sqrt{7}\).

Step3: Multiply by the coefficient outside the square root

We have the original expression \(4\sqrt{28}\), and we just found that \(\sqrt{28}=2\sqrt{7}\). So we multiply 4 by 2\(\sqrt{7}\), that is \(4\times2\sqrt{7}=8\sqrt{7}\).

Answer:

\(8\sqrt{7}\)