Question

simplify.
\sqrt{98}

Explanation:

Step1: Factor 98 into prime factors

We know that \( 98 = 49\times2 \), and \( 49 = 7^2 \), so \( 98 = 7^2\times2 \).

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

\(\sqrt{98}=\sqrt{7^2\times2}=\sqrt{7^2}\times\sqrt{2}\)

Step3: Simplify \(\sqrt{7^2}\)

Since \(\sqrt{a^2}=a\) for \(a\geq0\), then \(\sqrt{7^2} = 7\). So \(\sqrt{98}=7\sqrt{2}\)

Answer:

\(7\sqrt{2}\)