Solve sqrt{1+frac{19/81}-1-0.4519/81}{0.225}

$$\frac{ \sqrt{ 1+ \frac{ 19 }{ 81 } } -1-0.45 \frac{ 19 }{ 81 } }{ 0.225 }$$

Evaluate

$$-\frac{1858}{729}\approx -2.548696845$$

Solution Steps

Convert 1 to fraction \frac{81}{81}.

$$\frac{\sqrt{\frac{81}{81}+\frac{19}{81}}-1-\frac{0.45\times 81+19}{81}}{0.225}$$

Since \frac{81}{81} and \frac{19}{81} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{\frac{81+19}{81}}-1-\frac{0.45\times 81+19}{81}}{0.225}$$

Add 81 and 19 to get 100.

$$\frac{\sqrt{\frac{100}{81}}-1-\frac{0.45\times 81+19}{81}}{0.225}$$

Rewrite the square root of the division \frac{100}{81} as the division of square roots \frac{\sqrt{100}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\frac{10}{9}-1-\frac{0.45\times 81+19}{81}}{0.225}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{10}{9}-\frac{9}{9}-\frac{0.45\times 81+19}{81}}{0.225}$$

Since \frac{10}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-9}{9}-\frac{0.45\times 81+19}{81}}{0.225}$$

Subtract 9 from 10 to get 1.

$$\frac{\frac{1}{9}-\frac{0.45\times 81+19}{81}}{0.225}$$

Multiply 0.45 and 81 to get 36.45.

$$\frac{\frac{1}{9}-\frac{36.45+19}{81}}{0.225}$$

Add 36.45 and 19 to get 55.45.

$$\frac{\frac{1}{9}-\frac{55.45}{81}}{0.225}$$

Expand \frac{55.45}{81} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{1}{9}-\frac{5545}{8100}}{0.225}$$

Reduce the fraction \frac{5545}{8100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{9}-\frac{1109}{1620}}{0.225}$$

Least common multiple of 9 and 1620 is 1620. Convert \frac{1}{9} and \frac{1109}{1620} to fractions with denominator 1620.

$$\frac{\frac{180}{1620}-\frac{1109}{1620}}{0.225}$$

Since \frac{180}{1620} and \frac{1109}{1620} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{180-1109}{1620}}{0.225}$$

Subtract 1109 from 180 to get -929.

$$\frac{-\frac{929}{1620}}{0.225}$$

Express \frac{-\frac{929}{1620}}{0.225} as a single fraction.

$$\frac{-929}{1620\times 0.225}$$

Multiply 1620 and 0.225 to get 364.5.

$$\frac{-929}{364.5}$$

Expand \frac{-929}{364.5} by multiplying both numerator and the denominator by 10.

$$\frac{-9290}{3645}$$

Reduce the fraction \frac{-9290}{3645} to lowest terms by extracting and canceling out 5.

$$-\frac{1858}{729}$$

Factor

$$-\frac{1858}{729} = -2\frac{400}{729} = -2.5486968449931413$$