Solve (2/10-3/10*3/9)divsqrt{4/4-frac{3}{4}}-frac{2}{90}

$$( \frac{ 2 }{ 10 } - \frac{ 3 }{ 10 } \times \frac{ 3 }{ 9 } ) \div \sqrt{ \frac{ 4 }{ 4 } - \frac{ 3 }{ 4 } } - \frac{ 2 }{ 90 }$$

Evaluate

$$\frac{8}{45}\approx 0.177777778$$

Solution Steps

Divide 4 by 4 to get 1.

$$\frac{\frac{2}{10}-\frac{3}{10}\times \frac{3}{9}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{5}-\frac{3}{10}\times \frac{3}{9}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{5}-\frac{3}{10}\times \frac{1}{3}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Multiply \frac{3}{10} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{5}-\frac{3\times 1}{10\times 3}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{5}-\frac{1}{10}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{2}{10}-\frac{1}{10}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Since \frac{2}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-1}{10}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{1}{10}}{\sqrt{1-\frac{3}{4}}}-\frac{2}{90}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{1}{10}}{\sqrt{\frac{4}{4}-\frac{3}{4}}}-\frac{2}{90}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{10}}{\sqrt{\frac{4-3}{4}}}-\frac{2}{90}$$

Subtract 3 from 4 to get 1.

$$\frac{\frac{1}{10}}{\sqrt{\frac{1}{4}}}-\frac{2}{90}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{10}}{\frac{1}{2}}-\frac{2}{90}$$

Divide \frac{1}{10} by \frac{1}{2} by multiplying \frac{1}{10} by the reciprocal of \frac{1}{2}.

$$\frac{1}{10}\times 2-\frac{2}{90}$$

Multiply \frac{1}{10} and 2 to get \frac{2}{10}.

$$\frac{2}{10}-\frac{2}{90}$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}-\frac{2}{90}$$

Reduce the fraction \frac{2}{90} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}-\frac{1}{45}$$

Least common multiple of 5 and 45 is 45. Convert \frac{1}{5} and \frac{1}{45} to fractions with denominator 45.

$$\frac{9}{45}-\frac{1}{45}$$

Since \frac{9}{45} and \frac{1}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-1}{45}$$

Subtract 1 from 9 to get 8.

$$\frac{8}{45}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2} \cdot 5} = 0.17777777777777778$$