Question

simplify.
\sqrt{98}

Explanation:

Step1: Factor 98 into prime factors

We know that \(98 = 49\times2\), and \(49 = 7^2\). So we can rewrite \(\sqrt{98}\) as \(\sqrt{49\times2}\).

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

Applying this property to \(\sqrt{49\times2}\), we get \(\sqrt{49}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{49}\)

Since \(7^2 = 49\), then \(\sqrt{49}=7\). So \(\sqrt{49}\times\sqrt{2}=7\sqrt{2}\).

Answer:

\(7\sqrt{2}\)