Sure, let's solve this step-by-step.
1. Identify the given values:
- The numerator is [tex]\(3 \sqrt{12}\)[/tex].
- The denominator is [tex]\(\sqrt{3}\)[/tex].
2. Simplify the numerator:
- [tex]\( \sqrt{12} \)[/tex] can be simplified. Note that [tex]\(12 = 4 \times 3\)[/tex].
- Therefore, [tex]\( \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3} \)[/tex].
- So, [tex]\(3 \sqrt{12} = 3 \times 2 \sqrt{3} = 6 \sqrt{3}\)[/tex].
3. Set up the division:
- Now, we need to divide [tex]\(6 \sqrt{3}\)[/tex] by [tex]\(\sqrt{3}\)[/tex]:
[tex]\[
\frac{6 \sqrt{3}}{\sqrt{3}}
\][/tex]
4. Perform the division:
- Since [tex]\(\sqrt{3}\)[/tex] is present in both the numerator and the denominator, they cancel each other out:
[tex]\[
\frac{6 \sqrt{3}}{\sqrt{3}} = 6
\][/tex]
5. Conclusion:
- The result of the division [tex]\(3 \sqrt{12} \div \sqrt{3}\)[/tex] is [tex]\(6\)[/tex].
So, the complete simplified result is:
[tex]\[6\][/tex]
That's how you divide [tex]\(3 \sqrt{12}\)[/tex] by [tex]\(\sqrt{3}\)[/tex].
