Solve 1-sqrt{1/3:2/5-7/18}=

$$1 - \sqrt { \frac { 1 } { 3 } : \frac { 2 } { 5 } - \frac { 7 } { 18 } } =$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Divide \frac{1}{3} by \frac{2}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{2}{5}.

$$1-\sqrt{\frac{1}{3}\times \frac{5}{2}-\frac{7}{18}}$$

Multiply \frac{1}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$1-\sqrt{\frac{1\times 5}{3\times 2}-\frac{7}{18}}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 2}.

$$1-\sqrt{\frac{5}{6}-\frac{7}{18}}$$

Least common multiple of 6 and 18 is 18. Convert \frac{5}{6} and \frac{7}{18} to fractions with denominator 18.

$$1-\sqrt{\frac{15}{18}-\frac{7}{18}}$$

Since \frac{15}{18} and \frac{7}{18} have the same denominator, subtract them by subtracting their numerators.

$$1-\sqrt{\frac{15-7}{18}}$$

Subtract 7 from 15 to get 8.

$$1-\sqrt{\frac{8}{18}}$$

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

$$1-\sqrt{\frac{4}{9}}$$

Rewrite the square root of the division \frac{4}{9} as the division of square roots \frac{\sqrt{4}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$1-\frac{2}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{2}{3}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{3}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$