To simplify the radical expression [tex]\( \sqrt{48} \)[/tex], let’s break down the steps:
1. Factor 48 into its prime factors:
[tex]\[ 48 = 16 \times 3 \][/tex]
2. Simplify the square root:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3}
\][/tex]
[tex]\[
= \sqrt{16} \times \sqrt{3}
\][/tex]
3. Find the square root of 16:
[tex]\[
\sqrt{16} = 4
\][/tex]
4. Combine the results:
[tex]\[
\sqrt{48} = 4 \times \sqrt{3}
\][/tex]
So, the simplified form of [tex]\( \sqrt{48} \)[/tex] is [tex]\( 4 \sqrt{3} \)[/tex].
Given the options:
- [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].
