Solve 1-sqrt{1-(6*6713*10^-5)^2}

$$1 - \sqrt { 1 - ( 6 \cdot 6713 \times 10 ^ { - 5 } ) ^ { 2 } }$$

Evaluate

$$-\frac{\sqrt{2094420679}}{50000}+1\approx 0.084703178$$

Short Solution Steps

Multiply 6 and 6713 to get 40278.

$$1-\sqrt{1-\left(40278\times 10^{-5}\right)^{2}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$1-\sqrt{1-\left(40278\times \frac{1}{100000}\right)^{2}}$$

Multiply 40278 and \frac{1}{100000} to get \frac{20139}{50000}.

$$1-\sqrt{1-\left(\frac{20139}{50000}\right)^{2}}$$

Calculate \frac{20139}{50000} to the power of 2 and get \frac{405579321}{2500000000}.

$$1-\sqrt{1-\frac{405579321}{2500000000}}$$

Subtract \frac{405579321}{2500000000} from 1 to get \frac{2094420679}{2500000000}.

$$1-\sqrt{\frac{2094420679}{2500000000}}$$

Rewrite the square root of the division \sqrt{\frac{2094420679}{2500000000}} as the division of square roots \frac{\sqrt{2094420679}}{\sqrt{2500000000}}.

$$1-\frac{\sqrt{2094420679}}{\sqrt{2500000000}}$$

Calculate the square root of 2500000000 and get 50000.

$$1-\frac{\sqrt{2094420679}}{50000}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{50000}{50000}.

$$\frac{50000}{50000}-\frac{\sqrt{2094420679}}{50000}$$

Since \frac{50000}{50000} and \frac{\sqrt{2094420679}}{50000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{50000-\sqrt{2094420679}}{50000}$$

Factor

$$\frac{50000 - \sqrt{2094420679}}{50000} = 0.08470317841696844$$