Question

simplify.
\sqrt{50}

Explanation:

Step1: Factor 50 into prime factors

We know that \( 50 = 25\times2 \), and \( 25 = 5^2 \), so \( 50 = 5^2\times2 \).

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

For \( \sqrt{50} \), since \( 50 = 5^2\times2 \), we can write \( \sqrt{50}=\sqrt{5^2\times2} \).
According to the property \(\sqrt{a^2}=a\) (when \(a\geq0\)) and \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\), we have \(\sqrt{5^2\times2}=\sqrt{5^2}\times\sqrt{2}\).
Since \(\sqrt{5^2} = 5\), then \(\sqrt{5^2}\times\sqrt{2}=5\sqrt{2}\).

Answer:

\( 5\sqrt{2} \)