To simplify [tex]\(\sqrt{48}\)[/tex]:
1. Factorize the radicand (the number under the square root):
First, we express 48 as a product of factors, particularly looking for perfect squares. Notice that:
[tex]\[
48 = 16 \times 3
\][/tex]
where 16 is a perfect square.
2. Rewrite the square root using these factors:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3}
\][/tex]
3. Apply the property of square roots that allows us to separate the factors:
[tex]\[
\sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}
\][/tex]
4. Simplify the square root of the perfect square:
[tex]\[
\sqrt{16} = 4
\][/tex]
5. Combine the simplified square root with the remaining factor:
[tex]\[
\sqrt{48} = 4 \sqrt{3}
\][/tex]
Therefore, the simplified form of [tex]\(\sqrt{48}\)[/tex] is [tex]\(4 \sqrt{3}\)[/tex].
From the given choices:
- [tex]\(16 \sqrt{3}\)[/tex]
- [tex]\(4 \sqrt{3}\)[/tex]
- [tex]\(4 \sqrt{2}\)[/tex]
- [tex]\(6 \sqrt{2}\)[/tex]
The correct answer is [tex]\(4 \sqrt{3}\)[/tex], which corresponds to the second choice.
