Question

simplify the square root. assume all variables represent positive numbers. if the square root is already simplified, so state.
\sqrt{28}

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. \sqrt{28} = \square (type an exact answer, using radicals as needed.)
b. the expression is already simplified.

Explanation:

Step1: Factor the number inside the square root

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

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

Applying this property, we get \(\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}\).

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

Since \(\sqrt{4} = 2\) (because \(2^2 = 4\)), we substitute this back into the expression: \(2\times\sqrt{7}=2\sqrt{7}\).

Answer:

\(2\sqrt{7}\)