Solve frac{7^2-sqrt{25}}{2}+frac{8^2-sqrt{84}}{4}

$$\frac { 7 ^ { 2 } - \sqrt { 25 } } { 2 } + \frac { 8 ^ { 2 } - \sqrt { 84 } } { 4 }$$

Evaluate

$$-\frac{\sqrt{21}}{2}+38\approx 35.708712153$$

Short Solution Steps

Calculate 7 to the power of 2 and get 49.

$$\frac{49-\sqrt{25}}{2}+\frac{8^{2}-\sqrt{84}}{4}$$

Calculate the square root of 25 and get 5.

$$\frac{49-5}{2}+\frac{8^{2}-\sqrt{84}}{4}$$

Subtract 5 from 49 to get 44.

$$\frac{44}{2}+\frac{8^{2}-\sqrt{84}}{4}$$

Divide 44 by 2 to get 22.

$$22+\frac{8^{2}-\sqrt{84}}{4}$$

Calculate 8 to the power of 2 and get 64.

$$22+\frac{64-\sqrt{84}}{4}$$

Factor 84=2^{2}\times 21. Rewrite the square root of the product \sqrt{2^{2}\times 21} as the product of square roots \sqrt{2^{2}}\sqrt{21}. Take the square root of 2^{2}.

$$22+\frac{64-2\sqrt{21}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 22 times \frac{4}{4}.

$$\frac{22\times 4}{4}+\frac{64-2\sqrt{21}}{4}$$

Since \frac{22\times 4}{4} and \frac{64-2\sqrt{21}}{4} have the same denominator, add them by adding their numerators.

$$\frac{22\times 4+64-2\sqrt{21}}{4}$$

Do the multiplications in 22\times 4+64-2\sqrt{21}.

$$\frac{88+64-2\sqrt{21}}{4}$$

Do the calculations in 88+64-2\sqrt{21}.

$$\frac{152-2\sqrt{21}}{4}$$

Factor

$$\frac{76 - \sqrt{21}}{2} = 35.70871215252208$$