To simplify the radical expression [tex]\(\sqrt{48}\)[/tex], let's follow a step-by-step process:
1. Find the prime factorization of 48:
[tex]\[ 48 = 2^4 \cdot 3 \][/tex]
2. Rewrite the square root of 48 using its prime factors:
[tex]\[ \sqrt{48} = \sqrt{2^4 \cdot 3} \][/tex]
3. Group the factors under the square root sign in pairs of squares (since [tex]\(\sqrt{a^2} = a\)[/tex]):
[tex]\[ \sqrt{48} = \sqrt{(2^2)^2 \cdot 3} \][/tex]
4. Break the square root into the product of square roots:
[tex]\[ \sqrt{48} = \sqrt{(2^2)^2} \cdot \sqrt{3} \][/tex]
5. Simplify [tex]\(\sqrt{(2^2)^2}\)[/tex], which is equal to [tex]\(2^2\)[/tex] or 4:
[tex]\[ \sqrt{48} = 4 \cdot \sqrt{3} \][/tex]
Therefore, the simplified form of [tex]\(\sqrt{48}\)[/tex] is:
[tex]\[ 4 \sqrt{3} \][/tex]
Among the given options, the correct answer is:
[tex]\[ \boxed{4 \sqrt{3}} \][/tex]
