Multiply 9√3 ⋅6√7

give an exact answer

9 answers

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: \[ \boxed{54\sqrt{21}} \]

Multiply √ 11⋅6√ 7

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: \[ \boxed{6\sqrt{77}} \]

divide 2√ 65 / √ 5
provide and exact answer

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: \[ \boxed{2\sqrt{13}} \]

divide 9√ 33 / 27√ 11
provide exact answer

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: \[ \boxed{\frac{\sqrt{3}}{3}} \]

simplify 7√ 99

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: \[ \boxed{21\sqrt{11}} \]