Solve sqrt{20left(75^2+7^2right)+30left(65^2+10^2right)/50}

$$\sqrt{ \frac{ 20 \left( { 75 }^{ 2 } + { 7 }^{ 2 } \right) +30 \left( { 65 }^{ 2 } + { 10 }^{ 2 } \right) }{ 50 } }$$

Evaluate

$$\frac{\sqrt{121615}}{5}\approx 69.746684509$$

Solution Steps

Calculate 75 to the power of 2 and get 5625.

$$\sqrt{\frac{20\left(5625+7^{2}\right)+30\left(65^{2}+10^{2}\right)}{50}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{\frac{20\left(5625+49\right)+30\left(65^{2}+10^{2}\right)}{50}}$$

Add 5625 and 49 to get 5674.

$$\sqrt{\frac{20\times 5674+30\left(65^{2}+10^{2}\right)}{50}}$$

Multiply 20 and 5674 to get 113480.

$$\sqrt{\frac{113480+30\left(65^{2}+10^{2}\right)}{50}}$$

Calculate 65 to the power of 2 and get 4225.

$$\sqrt{\frac{113480+30\left(4225+10^{2}\right)}{50}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{113480+30\left(4225+100\right)}{50}}$$

Add 4225 and 100 to get 4325.

$$\sqrt{\frac{113480+30\times 4325}{50}}$$

Multiply 30 and 4325 to get 129750.

$$\sqrt{\frac{113480+129750}{50}}$$

Add 113480 and 129750 to get 243230.

$$\sqrt{\frac{243230}{50}}$$

Reduce the fraction \frac{243230}{50} to lowest terms by extracting and canceling out 10.

$$\sqrt{\frac{24323}{5}}$$

Rewrite the square root of the division \sqrt{\frac{24323}{5}} as the division of square roots \frac{\sqrt{24323}}{\sqrt{5}}.

$$\frac{\sqrt{24323}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{24323}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{24323}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{24323}\sqrt{5}}{5}$$

To multiply \sqrt{24323} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{121615}}{5}$$