Solve sqrt{(3/3-1/5-5/6)*1/7*(frac{5}{4}-frac{18}{8}+1)*frac{2}{5}}

$$\sqrt { ( \frac { 3 } { 3 } - \frac { 1 } { 5 } - \frac { 5 } { 6 } ) \cdot \frac { 1 } { 7 } \cdot ( \frac { 5 } { 4 } - \frac { 18 } { 8 } + 1 ) \cdot \frac { 2 } { 5 } }$$

Evaluate

$$0$$

Solution Steps

Divide 3 by 3 to get 1.

$$\sqrt{\left(1-\frac{1}{5}-\frac{5}{6}\right)\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\sqrt{\left(\frac{5}{5}-\frac{1}{5}-\frac{5}{6}\right)\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\left(\frac{5-1}{5}-\frac{5}{6}\right)\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Subtract 1 from 5 to get 4.

$$\sqrt{\left(\frac{4}{5}-\frac{5}{6}\right)\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{5}{6} to fractions with denominator 30.

$$\sqrt{\left(\frac{24}{30}-\frac{25}{30}\right)\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Since \frac{24}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{24-25}{30}\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Subtract 25 from 24 to get -1.

$$\sqrt{-\frac{1}{30}\times \frac{1}{7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Multiply -\frac{1}{30} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{-1}{30\times 7}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Do the multiplications in the fraction \frac{-1}{30\times 7}.

$$\sqrt{\frac{-1}{210}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Fraction \frac{-1}{210} can be rewritten as -\frac{1}{210} by extracting the negative sign.

$$\sqrt{-\frac{1}{210}\left(\frac{5}{4}-\frac{18}{8}+1\right)\times \frac{2}{5}}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$\sqrt{-\frac{1}{210}\left(\frac{5}{4}-\frac{9}{4}+1\right)\times \frac{2}{5}}$$

Since \frac{5}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{-\frac{1}{210}\left(\frac{5-9}{4}+1\right)\times \frac{2}{5}}$$

Subtract 9 from 5 to get -4.

$$\sqrt{-\frac{1}{210}\left(\frac{-4}{4}+1\right)\times \frac{2}{5}}$$

Divide -4 by 4 to get -1.

$$\sqrt{-\frac{1}{210}\left(-1+1\right)\times \frac{2}{5}}$$

Add -1 and 1 to get 0.

$$\sqrt{-\frac{1}{210}\times 0\times \frac{2}{5}}$$

Multiply -\frac{1}{210} and 0 to get 0.

$$\sqrt{0\times \frac{2}{5}}$$

Multiply 0 and \frac{2}{5} to get 0.

$$\sqrt{0}$$

Calculate the square root of 0 and get 0.

$$0$$

Factor

$$0$$