Question

write the expression so the radicand has no perfect squares other than 1.
\sqrt{28}

Explanation:

Step1: Factor 28 into prime factors

We know that \(28 = 4\times7\), where 4 is a perfect square (\(4 = 2^2\)).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

So, \(\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}\)

Step3: Simplify \(\sqrt{4}\)

Since \(\sqrt{4} = 2\), we have \(\sqrt{28}=2\sqrt{7}\)

Answer:

\(2\sqrt{7}\)