Solve sqrt{15/25-36/21+123/50}

$$\sqrt { \frac { 15 } { 25 } - \frac { 36 } { 21 } + \frac { 123 } { 50 } }$$

Evaluate

$$\frac{\sqrt{6594}}{70}\approx 1.16004926$$

Solution Steps

Reduce the fraction \frac{15}{25} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{3}{5}-\frac{36}{21}+\frac{123}{50}}$$

Reduce the fraction \frac{36}{21} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{3}{5}-\frac{12}{7}+\frac{123}{50}}$$

Least common multiple of 5 and 7 is 35. Convert \frac{3}{5} and \frac{12}{7} to fractions with denominator 35.

$$\sqrt{\frac{21}{35}-\frac{60}{35}+\frac{123}{50}}$$

Since \frac{21}{35} and \frac{60}{35} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{21-60}{35}+\frac{123}{50}}$$

Subtract 60 from 21 to get -39.

$$\sqrt{-\frac{39}{35}+\frac{123}{50}}$$

Least common multiple of 35 and 50 is 350. Convert -\frac{39}{35} and \frac{123}{50} to fractions with denominator 350.

$$\sqrt{-\frac{390}{350}+\frac{861}{350}}$$

Since -\frac{390}{350} and \frac{861}{350} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{-390+861}{350}}$$

Add -390 and 861 to get 471.

$$\sqrt{\frac{471}{350}}$$

Rewrite the square root of the division \sqrt{\frac{471}{350}} as the division of square roots \frac{\sqrt{471}}{\sqrt{350}}.

$$\frac{\sqrt{471}}{\sqrt{350}}$$

Factor 350=5^{2}\times 14. Rewrite the square root of the product \sqrt{5^{2}\times 14} as the product of square roots \sqrt{5^{2}}\sqrt{14}. Take the square root of 5^{2}.

$$\frac{\sqrt{471}}{5\sqrt{14}}$$

Rationalize the denominator of \frac{\sqrt{471}}{5\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{471}\sqrt{14}}{5\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{471}\sqrt{14}}{5\times 14}$$

To multiply \sqrt{471} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{6594}}{5\times 14}$$

Multiply 5 and 14 to get 70.

$$\frac{\sqrt{6594}}{70}$$