To simplify the expression [tex]\( 2 \sqrt{12} \times \sqrt{48} \)[/tex], we will perform a step-by-step breakdown of the simplification process.
1. Simplify the square roots individually:
- Simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3}
\][/tex]
- Simplify [tex]\(\sqrt{48}\)[/tex]:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4 \sqrt{3}
\][/tex]
2. Multiply the simplified forms of the square roots together:
- Combine [tex]\( \sqrt{12} \)[/tex] and [tex]\( \sqrt{48} \)[/tex]:
[tex]\[
(2 \sqrt{3}) \times (4 \sqrt{3}) = (2 \times 4) \times (\sqrt{3} \times \sqrt{3}) = 8 \times \sqrt{9}
\][/tex]
3. Simplify the expression further:
- Simplify [tex]\(\sqrt{9}\)[/tex]:
[tex]\[
\sqrt{9} = 3
\][/tex]
- Multiply the constants:
[tex]\[
8 \times 3 = 24
\][/tex]
Therefore, the simplifying steps lead us to the final simplified expression:
[tex]\[
2 \sqrt{12} \times \sqrt{48} = 24
\][/tex]
Thus, the simplified form of [tex]\( 2 \sqrt{12} \times \sqrt{48} \)[/tex] is [tex]\( 24 \)[/tex].
