Solve sqrt{1/0.94^2-1}

$$\sqrt{ \frac{ 1 }{ { 0.94 }^{ 2 } } -1 }$$

Evaluate

$$\frac{\sqrt{291}}{47}\approx 0.362951534$$

Solution Steps

Calculate 0.94 to the power of 2 and get 0.8836.

$$\sqrt{\frac{1}{0.8836}-1}$$

Expand \frac{1}{0.8836} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{10000}{8836}-1}$$

Reduce the fraction \frac{10000}{8836} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2500}{2209}-1}$$

Convert 1 to fraction \frac{2209}{2209}.

$$\sqrt{\frac{2500}{2209}-\frac{2209}{2209}}$$

Since \frac{2500}{2209} and \frac{2209}{2209} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{2500-2209}{2209}}$$

Subtract 2209 from 2500 to get 291.

$$\sqrt{\frac{291}{2209}}$$

Rewrite the square root of the division \sqrt{\frac{291}{2209}} as the division of square roots \frac{\sqrt{291}}{\sqrt{2209}}.

$$\frac{\sqrt{291}}{\sqrt{2209}}$$

Calculate the square root of 2209 and get 47.

$$\frac{\sqrt{291}}{47}$$