Solve sqrt{(1,8:2*2):[10*(0,6:2+1,8-0,1)]}

$$\sqrt { ( 1,8 : 2 \cdot 2 ) : [ 10 \cdot ( 0,6 : 2 + 1,8 - 0,1 ) ] }$$

Evaluate

$$0,3$$

Solution Steps

Expand \frac{1,8}{2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{\frac{18}{20}\times 2}{10\left(\frac{0,6}{2}+1,8-0,1\right)}}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{9}{10}\times 2}{10\left(\frac{0,6}{2}+1,8-0,1\right)}}$$

Express \frac{9}{10}\times 2 as a single fraction.

$$\sqrt{\frac{\frac{9\times 2}{10}}{10\left(\frac{0,6}{2}+1,8-0,1\right)}}$$

Multiply 9 and 2 to get 18.

$$\sqrt{\frac{\frac{18}{10}}{10\left(\frac{0,6}{2}+1,8-0,1\right)}}$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{0,6}{2}+1,8-0,1\right)}}$$

Expand \frac{0,6}{2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{6}{20}+1,8-0,1\right)}}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{3}{10}+1,8-0,1\right)}}$$

Convert decimal number 1,8 to fraction \frac{18}{10}. Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{3}{10}+\frac{9}{5}-0,1\right)}}$$

Least common multiple of 10 and 5 is 10. Convert \frac{3}{10} and \frac{9}{5} to fractions with denominator 10.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{3}{10}+\frac{18}{10}-0,1\right)}}$$

Since \frac{3}{10} and \frac{18}{10} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{3+18}{10}-0,1\right)}}$$

Add 3 and 18 to get 21.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{21}{10}-0,1\right)}}$$

Convert decimal number 0,1 to fraction \frac{1}{10}.

$$\sqrt{\frac{\frac{9}{5}}{10\left(\frac{21}{10}-\frac{1}{10}\right)}}$$

Since \frac{21}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{9}{5}}{10\times \frac{21-1}{10}}}$$

Subtract 1 from 21 to get 20.

$$\sqrt{\frac{\frac{9}{5}}{10\times \frac{20}{10}}}$$

Divide 20 by 10 to get 2.

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

Multiply 10 and 2 to get 20.

$$\sqrt{\frac{\frac{9}{5}}{20}}$$

Express \frac{\frac{9}{5}}{20} as a single fraction.

$$\sqrt{\frac{9}{5\times 20}}$$

Multiply 5 and 20 to get 100.

$$\sqrt{\frac{9}{100}}$$

Rewrite the square root of the division \frac{9}{100} as the division of square roots \frac{\sqrt{9}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$