To simplify [tex]\(\sqrt{48}\)[/tex], let's go through the steps systematically:
1. Factorize the number under the square root into its prime factors:
[tex]\[ 48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3 = 16 \times 3 \][/tex]
2. Rewrite the square root using the factors:
[tex]\[ \sqrt{48} = \sqrt{16 \times 3} \][/tex]
3. Utilize the property of square roots, which states [tex]\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)[/tex]:
[tex]\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} \][/tex]
4. Simplify the square root of 16:
[tex]\[ \sqrt{16} = 4 \][/tex]
5. Combine the simplified terms:
[tex]\[ \sqrt{48} = 4 \times \sqrt{3} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{48}\)[/tex] is:
[tex]\[ 4\sqrt{3} \][/tex]
So the correct answer is:
[tex]\[ 4 \sqrt{3} \][/tex]
