Question

factor each square root.
square root of 98

Answer 1

To factor the square root of 98, we start by breaking 98 down into its prime factors:

1. \( 98 = 2 \times 49 \)
2. \( 49 = 7 \times 7 \) or \( 49 = 7^2 \)

Now we can rewrite 98 as:

\[
98 = 2 \times 7^2
\]

Now we can express the square root of 98 as:

\[
\sqrt{98} = \sqrt{2 \times 7^2}
\]

Using the property of square roots that states \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can further simplify:

\[
\sqrt{98} = \sqrt{2} \times \sqrt{7^2}
\]

Since \(\sqrt{7^2} = 7\), we have:

\[
\sqrt{98} = 7\sqrt{2}
\]

So, the fully factored form of \(\sqrt{98}\) is:

\[
\sqrt{98} = 7\sqrt{2}
\]