Solve sqrt{2785/56}+56^2

$$\sqrt{ 2 \frac{ 785 }{ 56 } } + { 56 }^{ 2 }$$

Evaluate

$$\frac{\sqrt{12558}}{28}+3136\approx 3140.00223152$$

Short Solution Steps

Multiply 2 and 56 to get 112.

$$\sqrt{\frac{112+785}{56}}+56^{2}$$

Add 112 and 785 to get 897.

$$\sqrt{\frac{897}{56}}+56^{2}$$

Rewrite the square root of the division \sqrt{\frac{897}{56}} as the division of square roots \frac{\sqrt{897}}{\sqrt{56}}.

$$\frac{\sqrt{897}}{\sqrt{56}}+56^{2}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{\sqrt{897}}{2\sqrt{14}}+56^{2}$$

Rationalize the denominator of \frac{\sqrt{897}}{2\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{897}\sqrt{14}}{2\left(\sqrt{14}\right)^{2}}+56^{2}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{897}\sqrt{14}}{2\times 14}+56^{2}$$

To multiply \sqrt{897} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{12558}}{2\times 14}+56^{2}$$

Multiply 2 and 14 to get 28.

$$\frac{\sqrt{12558}}{28}+56^{2}$$

Calculate 56 to the power of 2 and get 3136.

$$\frac{\sqrt{12558}}{28}+3136$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3136 times \frac{28}{28}.

$$\frac{\sqrt{12558}}{28}+\frac{3136\times 28}{28}$$

Since \frac{\sqrt{12558}}{28} and \frac{3136\times 28}{28} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{12558}+3136\times 28}{28}$$

Do the multiplications in \sqrt{12558}+3136\times 28.

$$\frac{\sqrt{12558}+87808}{28}$$