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

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

Evaluate

$$\frac{3\sqrt{7}}{8}\approx 0.992156742$$

Solution Steps

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

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

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

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

Since \frac{64}{64} and \frac{1}{64} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 64 to get 63.

$$\sqrt{\frac{63}{64}}$$

Rewrite the square root of the division \sqrt{\frac{63}{64}} as the division of square roots \frac{\sqrt{63}}{\sqrt{64}}.

$$\frac{\sqrt{63}}{\sqrt{64}}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{3\sqrt{7}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$\frac{3\sqrt{7}}{8}$$