Solve sqrt{1-(13/14)^2}

$$\sqrt { 1 - ( \frac { 13 } { 14 } ) ^ { 2 } }$$

Evaluate

$$\frac{3\sqrt{3}}{14}\approx 0.371153744$$

Solution Steps

Calculate \frac{13}{14} to the power of 2 and get \frac{169}{196}.

$$\sqrt{1-\frac{169}{196}}$$

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

$$\sqrt{\frac{196}{196}-\frac{169}{196}}$$

Since \frac{196}{196} and \frac{169}{196} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{196-169}{196}}$$

Subtract 169 from 196 to get 27.

$$\sqrt{\frac{27}{196}}$$

Rewrite the square root of the division \sqrt{\frac{27}{196}} as the division of square roots \frac{\sqrt{27}}{\sqrt{196}}.

$$\frac{\sqrt{27}}{\sqrt{196}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Calculate the square root of 196 and get 14.

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