To simplify \(\sqrt{98}\), we start by factoring \(98\) into its prime factors.
First, we can break down \(98\) as follows:
\[ 98 = 2 \times 49 \]
Next, we recognize that \(49\) is a perfect square, as:
\[ 49 = 7^2 \]
Now we can rewrite \(\sqrt{98}\) using this factorization:
\[ \sqrt{98} = \sqrt{2 \times 49} = \sqrt{2 \times 7^2} \]
Using the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate this into two square roots:
\[ \sqrt{98} = \sqrt{2} \times \sqrt{7^2} \]
Since \(\sqrt{7^2} = 7\), we have:
\[ \sqrt{98} = \sqrt{2} \times 7 = 7\sqrt{2} \]
Thus, the simplified form of \(\sqrt{98}\) is:
\[ \boxed{7\sqrt{2}} \]
1 answer