Solve sqrt{(13/15+1/75+1/50)2/5}

$$\sqrt { ( \frac { 13 } { 15 } + \frac { 1 } { 75 } + \frac { 1 } { 50 } ) \frac { 2 } { 5 } }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

Least common multiple of 15 and 75 is 75. Convert \frac{13}{15} and \frac{1}{75} to fractions with denominator 75.

$$\sqrt{\left(\frac{65}{75}+\frac{1}{75}+\frac{1}{50}\right)\times \frac{2}{5}}$$

Since \frac{65}{75} and \frac{1}{75} have the same denominator, add them by adding their numerators.

$$\sqrt{\left(\frac{65+1}{75}+\frac{1}{50}\right)\times \frac{2}{5}}$$

Add 65 and 1 to get 66.

$$\sqrt{\left(\frac{66}{75}+\frac{1}{50}\right)\times \frac{2}{5}}$$

Reduce the fraction \frac{66}{75} to lowest terms by extracting and canceling out 3.

$$\sqrt{\left(\frac{22}{25}+\frac{1}{50}\right)\times \frac{2}{5}}$$

Least common multiple of 25 and 50 is 50. Convert \frac{22}{25} and \frac{1}{50} to fractions with denominator 50.

$$\sqrt{\left(\frac{44}{50}+\frac{1}{50}\right)\times \frac{2}{5}}$$

Since \frac{44}{50} and \frac{1}{50} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{44+1}{50}\times \frac{2}{5}}$$

Add 44 and 1 to get 45.

$$\sqrt{\frac{45}{50}\times \frac{2}{5}}$$

Reduce the fraction \frac{45}{50} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{9}{10}\times \frac{2}{5}}$$

Multiply \frac{9}{10} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{9\times 2}{10\times 5}}$$

Do the multiplications in the fraction \frac{9\times 2}{10\times 5}.

$$\sqrt{\frac{18}{50}}$$

Reduce the fraction \frac{18}{50} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{9}{25}}$$

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$