Question

simplify.
\sqrt{50}

Explanation:

Step1: Factor 50 into prime factors

We know that \(50 = 25\times2\), and \(25\) is a perfect square since \(25 = 5^{2}\). So we can rewrite \(\sqrt{50}\) as \(\sqrt{25\times2}\).

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

Applying the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) to \(\sqrt{25\times2}\), we get \(\sqrt{25}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{25}\)

Since \(\sqrt{25} = 5\) (because \(5\times5 = 25\)), then \(\sqrt{25}\times\sqrt{2}=5\sqrt{2}\).

Answer:

\(5\sqrt{2}\)