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

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

Evaluate

$$\frac{\sqrt{55}}{8}\approx 0.927024811$$

Solution Steps

Calculate \frac{3}{8} to the power of 2 and get \frac{9}{64}.

$$\sqrt{1-\frac{9}{64}}$$

Convert 1 to fraction \frac{64}{64}.

$$\sqrt{\frac{64}{64}-\frac{9}{64}}$$

Since \frac{64}{64} and \frac{9}{64} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{64-9}{64}}$$

Subtract 9 from 64 to get 55.

$$\sqrt{\frac{55}{64}}$$

Rewrite the square root of the division \sqrt{\frac{55}{64}} as the division of square roots \frac{\sqrt{55}}{\sqrt{64}}.

$$\frac{\sqrt{55}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$\frac{\sqrt{55}}{8}$$