To solve the expression [tex]\(5 \sqrt{12} \times 3 \sqrt{75}\)[/tex], let's go through it step-by-step:
1. Simplify each square root individually:
- For [tex]\(\sqrt{12}\)[/tex]:
[tex]\[\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}\][/tex]
- For [tex]\(\sqrt{75}\)[/tex]:
[tex]\[\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}\][/tex]
2. Multiply the simplified forms:
Now, substitute these simplified forms back into the original expression:
- First, calculate [tex]\(\sqrt{12} \times \sqrt{75}\)[/tex]:
[tex]\[
(2\sqrt{3}) \times (5\sqrt{3}) = 2 \times 5 \times \sqrt{3} \times \sqrt{3} = 10 \times 3 = 30
\][/tex]
3. Multiply by the coefficients:
Now, recall that the original expression includes the coefficients [tex]\(5\)[/tex] and [tex]\(3\)[/tex]:
[tex]\[
5 \times 3 = 15
\][/tex]
4. Combine everything together:
Multiply the result from step 2 with the product of the coefficients:
[tex]\[
15 \times 30 = 450
\][/tex]
So, the final result of the expression [tex]\(5 \sqrt{12} \times 3 \sqrt{75}\)[/tex] is [tex]\(450\)[/tex].
