Solve sqrt{72^2+104^2/25^2}

$$\sqrt { \frac { 72 ^ { 2 } + 104 ^ { 2 } } { 25 ^ { 2 } } }$$

Evaluate

$$\frac{8\sqrt{10}}{5}\approx 5.059644256$$

Solution Steps

Calculate 72 to the power of 2 and get 5184.

$$\sqrt{\frac{5184+104^{2}}{25^{2}}}$$

Calculate 104 to the power of 2 and get 10816.

$$\sqrt{\frac{5184+10816}{25^{2}}}$$

Add 5184 and 10816 to get 16000.

$$\sqrt{\frac{16000}{25^{2}}}$$

Calculate 25 to the power of 2 and get 625.

$$\sqrt{\frac{16000}{625}}$$

Reduce the fraction \frac{16000}{625} to lowest terms by extracting and canceling out 125.

$$\sqrt{\frac{128}{5}}$$

Rewrite the square root of the division \sqrt{\frac{128}{5}} as the division of square roots \frac{\sqrt{128}}{\sqrt{5}}.

$$\frac{\sqrt{128}}{\sqrt{5}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{8\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{8\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{8\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{8\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{8\sqrt{10}}{5}$$