Solve sqrt{0,3+(3/8-4/15+1,5-1/40)*(1-15/19)}

$$\sqrt { 0,3 + ( \frac { 3 } { 8 } - \frac { 4 } { 15 } + 1,5 - \frac { 1 } { 40 } ) \times ( 1 - \frac { 15 } { 19 } ) }$$

Evaluate

$$\frac{\sqrt{570}}{30}\approx 0.795822426$$

Solution Steps

Least common multiple of 8 and 15 is 120. Convert \frac{3}{8} and \frac{4}{15} to fractions with denominator 120.

$$\sqrt{0,3+\left(\frac{45}{120}-\frac{32}{120}+1,5-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Since \frac{45}{120} and \frac{32}{120} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{0,3+\left(\frac{45-32}{120}+1,5-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Subtract 32 from 45 to get 13.

$$\sqrt{0,3+\left(\frac{13}{120}+1,5-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Convert decimal number 1,5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\sqrt{0,3+\left(\frac{13}{120}+\frac{3}{2}-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Least common multiple of 120 and 2 is 120. Convert \frac{13}{120} and \frac{3}{2} to fractions with denominator 120.

$$\sqrt{0,3+\left(\frac{13}{120}+\frac{180}{120}-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Since \frac{13}{120} and \frac{180}{120} have the same denominator, add them by adding their numerators.

$$\sqrt{0,3+\left(\frac{13+180}{120}-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Add 13 and 180 to get 193.

$$\sqrt{0,3+\left(\frac{193}{120}-\frac{1}{40}\right)\left(1-\frac{15}{19}\right)}$$

Least common multiple of 120 and 40 is 120. Convert \frac{193}{120} and \frac{1}{40} to fractions with denominator 120.

$$\sqrt{0,3+\left(\frac{193}{120}-\frac{3}{120}\right)\left(1-\frac{15}{19}\right)}$$

Since \frac{193}{120} and \frac{3}{120} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{0,3+\frac{193-3}{120}\left(1-\frac{15}{19}\right)}$$

Subtract 3 from 193 to get 190.

$$\sqrt{0,3+\frac{190}{120}\left(1-\frac{15}{19}\right)}$$

Reduce the fraction \frac{190}{120} to lowest terms by extracting and canceling out 10.

$$\sqrt{0,3+\frac{19}{12}\left(1-\frac{15}{19}\right)}$$

Convert 1 to fraction \frac{19}{19}.

$$\sqrt{0,3+\frac{19}{12}\left(\frac{19}{19}-\frac{15}{19}\right)}$$

Since \frac{19}{19} and \frac{15}{19} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{0,3+\frac{19}{12}\times \frac{19-15}{19}}$$

Subtract 15 from 19 to get 4.

$$\sqrt{0,3+\frac{19}{12}\times \frac{4}{19}}$$

Multiply \frac{19}{12} times \frac{4}{19} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{0,3+\frac{19\times 4}{12\times 19}}$$

Cancel out 19 in both numerator and denominator.

$$\sqrt{0,3+\frac{4}{12}}$$

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

$$\sqrt{0,3+\frac{1}{3}}$$

Convert decimal number 0,3 to fraction \frac{3}{10}.

$$\sqrt{\frac{3}{10}+\frac{1}{3}}$$

Least common multiple of 10 and 3 is 30. Convert \frac{3}{10} and \frac{1}{3} to fractions with denominator 30.

$$\sqrt{\frac{9}{30}+\frac{10}{30}}$$

Since \frac{9}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{9+10}{30}}$$

Add 9 and 10 to get 19.

$$\sqrt{\frac{19}{30}}$$

Rewrite the square root of the division \sqrt{\frac{19}{30}} as the division of square roots \frac{\sqrt{19}}{\sqrt{30}}.

$$\frac{\sqrt{19}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{19}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{19}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{19}\sqrt{30}}{30}$$

To multiply \sqrt{19} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{570}}{30}$$