Solve sqrt{1-(5/14)^2}

$$\sqrt { 1 - ( \frac { 5 } { 14 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{19}}{14}\approx 0.934049774$$

Solution Steps

Calculate \frac{5}{14} to the power of 2 and get \frac{25}{196}.

$$\sqrt{1-\frac{25}{196}}$$

Convert 1 to fraction \frac{196}{196}.

$$\sqrt{\frac{196}{196}-\frac{25}{196}}$$

Since \frac{196}{196} and \frac{25}{196} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{196-25}{196}}$$

Subtract 25 from 196 to get 171.

$$\sqrt{\frac{171}{196}}$$

Rewrite the square root of the division \sqrt{\frac{171}{196}} as the division of square roots \frac{\sqrt{171}}{\sqrt{196}}.

$$\frac{\sqrt{171}}{\sqrt{196}}$$

Factor 171=3^{2}\times 19. Rewrite the square root of the product \sqrt{3^{2}\times 19} as the product of square roots \sqrt{3^{2}}\sqrt{19}. Take the square root of 3^{2}.

$$\frac{3\sqrt{19}}{\sqrt{196}}$$

Calculate the square root of 196 and get 14.

$$\frac{3\sqrt{19}}{14}$$