Simplify 48−−√

1 answer

To simplify \(\sqrt{48}\), we can start by factoring 48 into its prime factors:

\[ 48 = 16 \times 3 = 4^2 \times 3 \]

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

\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} \]

Since \(\sqrt{16} = 4\), we can simplify it further:

\[ \sqrt{48} = 4 \times \sqrt{3} \]

Therefore, the simplified form of \(\sqrt{48}\) is:

\[ \boxed{4\sqrt{3}} \]