Solve 165*sqrt{8/7}*10

$$165 \times \sqrt { 8 / 7 } \times 10$$

Evaluate

$$\frac{3300\sqrt{14}}{7}\approx 1763.924196622$$

Solution Steps

Multiply 10 and 165 to get 1650.

$$1650\sqrt{\frac{8}{7}}$$

Rewrite the square root of the division \sqrt{\frac{8}{7}} as the division of square roots \frac{\sqrt{8}}{\sqrt{7}}.

$$1650\times \frac{\sqrt{8}}{\sqrt{7}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$1650\times \frac{2\sqrt{2}}{\sqrt{7}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$1650\times \frac{2\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$1650\times \frac{2\sqrt{2}\sqrt{7}}{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$1650\times \frac{2\sqrt{14}}{7}$$

Express 1650\times \frac{2\sqrt{14}}{7} as a single fraction.

$$\frac{1650\times 2\sqrt{14}}{7}$$

Multiply 1650 and 2 to get 3300.

$$\frac{3300\sqrt{14}}{7}$$