Solve -frac{sqrt{(20^2)+2(981)(40)-2(981)(0)+20}}{981}

$$- \frac{ \sqrt{ ( { 20 }^{ 2 } )+2(981)(40)-2(981)(0)+20 } }{ 981 }$$

Evaluate

$$-\frac{10\sqrt{789}}{981}\approx -0.286331741$$

Solution Steps

Calculate 20 to the power of 2 and get 400.

$$-\frac{\sqrt{400+2\times 981\times 40-2\times 981\times 0+20}}{981}$$

Multiply 2 and 981 to get 1962.

$$-\frac{\sqrt{400+1962\times 40-2\times 981\times 0+20}}{981}$$

Multiply 1962 and 40 to get 78480.

$$-\frac{\sqrt{400+78480-2\times 981\times 0+20}}{981}$$

Add 400 and 78480 to get 78880.

$$-\frac{\sqrt{78880-2\times 981\times 0+20}}{981}$$

Multiply 2 and 981 to get 1962.

$$-\frac{\sqrt{78880-1962\times 0+20}}{981}$$

Multiply 1962 and 0 to get 0.

$$-\frac{\sqrt{78880-0+20}}{981}$$

Subtract 0 from 78880 to get 78880.

$$-\frac{\sqrt{78880+20}}{981}$$

Add 78880 and 20 to get 78900.

$$-\frac{\sqrt{78900}}{981}$$

Factor 78900=10^{2}\times 789. Rewrite the square root of the product \sqrt{10^{2}\times 789} as the product of square roots \sqrt{10^{2}}\sqrt{789}. Take the square root of 10^{2}.

$$-\frac{10\sqrt{789}}{981}$$