Solve sqrt{3640^2+2160^2/14}

$$\sqrt { \frac { 3640 ^ { 2 } + 2160 ^ { 2 } } { 14 } }$$

Evaluate

$$\frac{20\sqrt{156758}}{7}\approx 1131.219316869$$

Solution Steps

Calculate 3640 to the power of 2 and get 13249600.

$$\sqrt{\frac{13249600+2160^{2}}{14}}$$

Calculate 2160 to the power of 2 and get 4665600.

$$\sqrt{\frac{13249600+4665600}{14}}$$

Add 13249600 and 4665600 to get 17915200.

$$\sqrt{\frac{17915200}{14}}$$

Reduce the fraction \frac{17915200}{14} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{8957600}{7}}$$

Rewrite the square root of the division \sqrt{\frac{8957600}{7}} as the division of square roots \frac{\sqrt{8957600}}{\sqrt{7}}.

$$\frac{\sqrt{8957600}}{\sqrt{7}}$$

Factor 8957600=20^{2}\times 22394. Rewrite the square root of the product \sqrt{20^{2}\times 22394} as the product of square roots \sqrt{20^{2}}\sqrt{22394}. Take the square root of 20^{2}.

$$\frac{20\sqrt{22394}}{\sqrt{7}}$$

Rationalize the denominator of \frac{20\sqrt{22394}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{20\sqrt{22394}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{20\sqrt{22394}\sqrt{7}}{7}$$

To multiply \sqrt{22394} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{20\sqrt{156758}}{7}$$