Solve sqrt{1+400/169-40/65}

$$\sqrt { 1 + \frac { 400 } { 169 } - \frac { 40 } { 65 } }$$

Evaluate

$$\frac{\sqrt{465}}{13}\approx 1.658758358$$

Solution Steps

Convert 1 to fraction \frac{169}{169}.

$$\sqrt{\frac{169}{169}+\frac{400}{169}-\frac{40}{65}}$$

Since \frac{169}{169} and \frac{400}{169} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{169+400}{169}-\frac{40}{65}}$$

Add 169 and 400 to get 569.

$$\sqrt{\frac{569}{169}-\frac{40}{65}}$$

Reduce the fraction \frac{40}{65} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{569}{169}-\frac{8}{13}}$$

Least common multiple of 169 and 13 is 169. Convert \frac{569}{169} and \frac{8}{13} to fractions with denominator 169.

$$\sqrt{\frac{569}{169}-\frac{104}{169}}$$

Since \frac{569}{169} and \frac{104}{169} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{569-104}{169}}$$

Subtract 104 from 569 to get 465.

$$\sqrt{\frac{465}{169}}$$

Rewrite the square root of the division \sqrt{\frac{465}{169}} as the division of square roots \frac{\sqrt{465}}{\sqrt{169}}.

$$\frac{\sqrt{465}}{\sqrt{169}}$$

Calculate the square root of 169 and get 13.

$$\frac{\sqrt{465}}{13}$$