Solve sqrt{1-(9/16)^2}

$$\sqrt { 1 - ( \frac { 9 } { 16 } ) ^ { 2 } }$$

Evaluate

$$\frac{5\sqrt{7}}{16}\approx 0.826797285$$

Solution Steps

Calculate \frac{9}{16} to the power of 2 and get \frac{81}{256}.

$$\sqrt{1-\frac{81}{256}}$$

Convert 1 to fraction \frac{256}{256}.

$$\sqrt{\frac{256}{256}-\frac{81}{256}}$$

Since \frac{256}{256} and \frac{81}{256} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{256-81}{256}}$$

Subtract 81 from 256 to get 175.

$$\sqrt{\frac{175}{256}}$$

Rewrite the square root of the division \sqrt{\frac{175}{256}} as the division of square roots \frac{\sqrt{175}}{\sqrt{256}}.

$$\frac{\sqrt{175}}{\sqrt{256}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{5\sqrt{7}}{\sqrt{256}}$$

Calculate the square root of 256 and get 16.

$$\frac{5\sqrt{7}}{16}$$