Answered

Select the correct answer.

Simplify.

[tex]\[ \sqrt{48} \][/tex]

A. [tex]\(16 \sqrt{3}\)[/tex]
B. 24
C. [tex]\(4 \sqrt{2}\)[/tex]
D. [tex]\(4 \sqrt{3}\)[/tex]



Answer :

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]