Question

question
express in simplest radical form.
\\(\sqrt{20}\\)
answer attempt 1 out of 2

Explanation:

Step1: Factor the radicand

Factor 20 into a product of a perfect square and another number. We know that \(20 = 4\times5\), where 4 is a perfect square. So, \(\sqrt{20}=\sqrt{4\times5}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{4\times5}\) as \(\sqrt{4}\times\sqrt{5}\).

Step3: Simplify the perfect square root

Since \(\sqrt{4} = 2\), we substitute that back in. So, \(\sqrt{4}\times\sqrt{5}=2\times\sqrt{5}=2\sqrt{5}\).

Answer:

\(2\sqrt{5}\)