Solve sqrt{1-65/65^2}

$$\sqrt { 1 - \frac { 65 } { 65 ^ { 2 } } }$$

Evaluate

$$\frac{8\sqrt{65}}{65}\approx 0.992277877$$

Solution Steps

Rewrite 65^{2} as 65\times 65. Cancel out 65 in both numerator and denominator.

$$\sqrt{1-\frac{1}{65}}$$

Convert 1 to fraction \frac{65}{65}.

$$\sqrt{\frac{65}{65}-\frac{1}{65}}$$

Since \frac{65}{65} and \frac{1}{65} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{65-1}{65}}$$

Subtract 1 from 65 to get 64.

$$\sqrt{\frac{64}{65}}$$

Rewrite the square root of the division \sqrt{\frac{64}{65}} as the division of square roots \frac{\sqrt{64}}{\sqrt{65}}.

$$\frac{\sqrt{64}}{\sqrt{65}}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{\sqrt{65}}$$

Rationalize the denominator of \frac{8}{\sqrt{65}} by multiplying numerator and denominator by \sqrt{65}.

$$\frac{8\sqrt{65}}{\left(\sqrt{65}\right)^{2}}$$

The square of \sqrt{65} is 65.

$$\frac{8\sqrt{65}}{65}$$