Solve sqrt{1-100^2/(3*10^8)^2}

$$\sqrt { 1 - \frac { 100 ^ { 2 } } { ( 3 \times 10 ^ { 8 } ) ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{8999999999999}}{3000000}\approx 1$$

Solution Steps

Calculate 100 to the power of 2 and get 10000.

$$\sqrt{1-\frac{10000}{\left(3\times 10^{8}\right)^{2}}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\sqrt{1-\frac{10000}{\left(3\times 100000000\right)^{2}}}$$

Multiply 3 and 100000000 to get 300000000.

$$\sqrt{1-\frac{10000}{300000000^{2}}}$$

Calculate 300000000 to the power of 2 and get 90000000000000000.

$$\sqrt{1-\frac{10000}{90000000000000000}}$$

Reduce the fraction \frac{10000}{90000000000000000} to lowest terms by extracting and canceling out 10000.

$$\sqrt{1-\frac{1}{9000000000000}}$$

Subtract \frac{1}{9000000000000} from 1 to get \frac{8999999999999}{9000000000000}.

$$\sqrt{\frac{8999999999999}{9000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{8999999999999}{9000000000000}} as the division of square roots \frac{\sqrt{8999999999999}}{\sqrt{9000000000000}}.

$$\frac{\sqrt{8999999999999}}{\sqrt{9000000000000}}$$

Calculate the square root of 9000000000000 and get 3000000.

$$\frac{\sqrt{8999999999999}}{3000000}$$