Solve frac{70+80*sqrt{90}-100}{pi}

$$\frac { 70 + 80 \times \sqrt { 90 } - 100 } { \pi }$$

Evaluate

$$\frac{30\left(8\sqrt{10}-1\right)}{\pi }\approx 232.030921516$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{70+80\times 3\sqrt{10}-100}{\pi }$$

Multiply 80 and 3 to get 240.

$$\frac{70+240\sqrt{10}-100}{\pi }$$

Subtract 100 from 70 to get -30.

$$\frac{-30+240\sqrt{10}}{\pi }$$

Factor

$$\frac{30 {(8 \sqrt{10} - 1)}}{\pi} = 232.03092151602408$$