Solve sqrt{1-17^2/18^2}

$$\sqrt { 1 - \frac { 17 ^ { 2 } } { 18 ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{35}}{18}\approx 0.328671099$$

Solution Steps

Calculate 17 to the power of 2 and get 289.

$$\sqrt{1-\frac{289}{18^{2}}}$$

Calculate 18 to the power of 2 and get 324.

$$\sqrt{1-\frac{289}{324}}$$

Convert 1 to fraction \frac{324}{324}.

$$\sqrt{\frac{324}{324}-\frac{289}{324}}$$

Since \frac{324}{324} and \frac{289}{324} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{324-289}{324}}$$

Subtract 289 from 324 to get 35.

$$\sqrt{\frac{35}{324}}$$

Rewrite the square root of the division \sqrt{\frac{35}{324}} as the division of square roots \frac{\sqrt{35}}{\sqrt{324}}.

$$\frac{\sqrt{35}}{\sqrt{324}}$$

Calculate the square root of 324 and get 18.

$$\frac{\sqrt{35}}{18}$$