Asked by Someone__:)

Multiply 9√3 ⋅6√7
give an exact answer
Answered by Someone__:)
Multiply √ 11⋅6√ 7
Answered by Someone__:)
divide 2√ 65 / √ 5
provide and exact answer
Answered by Someone__:)
divide 9√ 33 / 27√ 11
provide exact answer
Answered by Someone__:)
simplify 7√ 99
Answered by GPT-4o mini
To multiply \( 9\sqrt{3} \) and \( 6\sqrt{7} \), you can multiply the coefficients (the numbers outside the square roots) and the square roots separately.

1. Multiply the coefficients:
\[
9 \times 6 = 54
\]

2. Multiply the square roots:
\[
\sqrt{3} \times \sqrt{7} = \sqrt{3 \times 7} = \sqrt{21}
\]

Now combine the results:
\[
9\sqrt{3} \cdot 6\sqrt{7} = 54\sqrt{21}
\]

Thus, the exact answer is:
\[
\boxed{54\sqrt{21}}
\]
Answered by GPT-4o mini
To multiply \( \sqrt{11} \) and \( 6\sqrt{7} \), follow these steps:

1. Multiply the coefficients:
\[
6
\]

2. Multiply the square roots:
\[
\sqrt{11} \cdot \sqrt{7} = \sqrt{11 \cdot 7} = \sqrt{77}
\]

Now combine the results:
\[
\sqrt{11} \cdot 6\sqrt{7} = 6\sqrt{77}
\]

Thus, the exact answer is:
\[
\boxed{6\sqrt{77}}
\]
Answered by GPT-4o mini
To divide \( \frac{2\sqrt{65}}{\sqrt{5}} \), you can simplify it by following these steps:

1. Simplify the expression by dividing the square roots:
\[
\frac{2\sqrt{65}}{\sqrt{5}} = 2 \cdot \frac{\sqrt{65}}{\sqrt{5}} = 2 \cdot \sqrt{\frac{65}{5}}
\]

2. Simplify the fraction under the square root:
\[
\frac{65}{5} = 13
\]
So,
\[
\sqrt{\frac{65}{5}} = \sqrt{13}
\]

3. Now combine the results:
\[
2\sqrt{13}
\]

Thus, the exact answer is:
\[
\boxed{2\sqrt{13}}
\]
Answered by GPT-4o mini
To divide \( \frac{9\sqrt{33}}{27\sqrt{11}} \), follow these steps:

1. **Divide the coefficients**:
\[
\frac{9}{27} = \frac{1}{3}
\]

2. **Divide the square roots**:
\[
\frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3}
\]

3. **Combine the results**:
\[
\frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3}\sqrt{3}
\]

Thus, the exact answer is:
\[
\boxed{\frac{\sqrt{3}}{3}}
\]
Answered by GPT-4o mini
To simplify \( 7\sqrt{99} \), we can first simplify the square root:

1. Factor \( 99 \):
\[
99 = 9 \times 11
\]
Since \( 9 \) is a perfect square, we can take the square root of it.

2. Rewrite the square root:
\[
\sqrt{99} = \sqrt{9 \times 11} = \sqrt{9} \times \sqrt{11} = 3\sqrt{11}
\]

3. Now substitute back into the expression:
\[
7\sqrt{99} = 7 \times 3\sqrt{11} = 21\sqrt{11}
\]

Thus, the simplified form of \( 7\sqrt{99} \) is:
\[
\boxed{21\sqrt{11}}
\]