Question

simplify.
\sqrt{50}

Explanation:

Step1: Factor 50 into prime factors

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

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

Applying this property, we have \(\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}\).

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

Since \(5^2 = 25\), then \(\sqrt{25}=5\). So \(\sqrt{25}\times\sqrt{2}=5\sqrt{2}\).

Answer:

\(5\sqrt{2}\)