Solve frac{sqrt{5^52}-32/7+(5-3^2)}{2}

$$\frac { \sqrt { 5 ^ { 5 } 2 } - \frac { 32 } { 7 } + ( 5 - 3 ^ { 2 } ) } { 2 }$$

Evaluate

$$\frac{25\sqrt{10}}{2}-\frac{30}{7}\approx 35.242756466$$

Solution Steps

Calculate 5 to the power of 5 and get 3125.

$$\frac{\sqrt{3125\times 2}-\frac{32}{7}+5-3^{2}}{2}$$

Multiply 3125 and 2 to get 6250.

$$\frac{\sqrt{6250}-\frac{32}{7}+5-3^{2}}{2}$$

Factor 6250=25^{2}\times 10. Rewrite the square root of the product \sqrt{25^{2}\times 10} as the product of square roots \sqrt{25^{2}}\sqrt{10}. Take the square root of 25^{2}.

$$\frac{25\sqrt{10}-\frac{32}{7}+5-3^{2}}{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{25\sqrt{10}-\frac{32}{7}+5-9}{2}$$

Subtract 9 from 5 to get -4.

$$\frac{25\sqrt{10}-\frac{32}{7}-4}{2}$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{25\sqrt{10}-\frac{32}{7}-\frac{28}{7}}{2}$$

Since -\frac{32}{7} and \frac{28}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\sqrt{10}+\frac{-32-28}{7}}{2}$$

Subtract 28 from -32 to get -60.

$$\frac{25\sqrt{10}-\frac{60}{7}}{2}$$

Factor

$$\frac{5 {(35 \sqrt{10} - 12)}}{14} = 35.24275646639046$$