Solve sqrt{35/26-12/76-5/9})+(110/77)

$$\sqrt { \frac { 35 } { 26 } - \frac { 12 } { 76 } - \frac { 5 } { 9 } } ) + ( 1 \frac { 10 } { 77 } )$$

Evaluate

$$\frac{\sqrt{1389622}}{1482}\approx 0.795426649$$

Solution Steps

Reduce the fraction \frac{12}{76} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{35}{26}-\frac{3}{19}-\frac{5}{9}}$$

Least common multiple of 26 and 19 is 494. Convert \frac{35}{26} and \frac{3}{19} to fractions with denominator 494.

$$\sqrt{\frac{665}{494}-\frac{78}{494}-\frac{5}{9}}$$

Since \frac{665}{494} and \frac{78}{494} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{665-78}{494}-\frac{5}{9}}$$

Subtract 78 from 665 to get 587.

$$\sqrt{\frac{587}{494}-\frac{5}{9}}$$

Least common multiple of 494 and 9 is 4446. Convert \frac{587}{494} and \frac{5}{9} to fractions with denominator 4446.

$$\sqrt{\frac{5283}{4446}-\frac{2470}{4446}}$$

Since \frac{5283}{4446} and \frac{2470}{4446} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{5283-2470}{4446}}$$

Subtract 2470 from 5283 to get 2813.

$$\sqrt{\frac{2813}{4446}}$$

Rewrite the square root of the division \sqrt{\frac{2813}{4446}} as the division of square roots \frac{\sqrt{2813}}{\sqrt{4446}}.

$$\frac{\sqrt{2813}}{\sqrt{4446}}$$

Factor 4446=3^{2}\times 494. Rewrite the square root of the product \sqrt{3^{2}\times 494} as the product of square roots \sqrt{3^{2}}\sqrt{494}. Take the square root of 3^{2}.

$$\frac{\sqrt{2813}}{3\sqrt{494}}$$

Rationalize the denominator of \frac{\sqrt{2813}}{3\sqrt{494}} by multiplying numerator and denominator by \sqrt{494}.

$$\frac{\sqrt{2813}\sqrt{494}}{3\left(\sqrt{494}\right)^{2}}$$

The square of \sqrt{494} is 494.

$$\frac{\sqrt{2813}\sqrt{494}}{3\times 494}$$

To multiply \sqrt{2813} and \sqrt{494}, multiply the numbers under the square root.

$$\frac{\sqrt{1389622}}{3\times 494}$$

Multiply 3 and 494 to get 1482.

$$\frac{\sqrt{1389622}}{1482}$$