Solve sqrt{1-(16/65)^2}

$$\sqrt { 1 - ( \frac { 16 } { 65 } ) ^ { 2 } }$$

Evaluate

$$\frac{63}{65}\approx 0.969230769$$

Solution Steps

Calculate \frac{16}{65} to the power of 2 and get \frac{256}{4225}.

$$\sqrt{1-\frac{256}{4225}}$$

Convert 1 to fraction \frac{4225}{4225}.

$$\sqrt{\frac{4225}{4225}-\frac{256}{4225}}$$

Since \frac{4225}{4225} and \frac{256}{4225} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{4225-256}{4225}}$$

Subtract 256 from 4225 to get 3969.

$$\sqrt{\frac{3969}{4225}}$$

Rewrite the square root of the division \frac{3969}{4225} as the division of square roots \frac{\sqrt{3969}}{\sqrt{4225}}. Take the square root of both numerator and denominator.

$$\frac{63}{65}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{5 \cdot 13} = 0.9692307692307692$$