Solve sqrt{4/81}:sqrt{25/81}-12/5

$$\sqrt { \frac { 4 } { 81 } } : \sqrt { \frac { 25 } { 81 } } - 1 \frac { 2 } { 5 }$$

Evaluate

$$-1$$

Solution Steps

Rewrite the square root of the division \frac{4}{81} as the division of square roots \frac{\sqrt{4}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\frac{2}{9}}{\sqrt{\frac{25}{81}}}-\frac{1\times 5+2}{5}$$

Rewrite the square root of the division \frac{25}{81} as the division of square roots \frac{\sqrt{25}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{\frac{2}{9}}{\frac{5}{9}}-\frac{1\times 5+2}{5}$$

Divide \frac{2}{9} by \frac{5}{9} by multiplying \frac{2}{9} by the reciprocal of \frac{5}{9}.

$$\frac{2}{9}\times \frac{9}{5}-\frac{1\times 5+2}{5}$$

Multiply \frac{2}{9} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 9}{9\times 5}-\frac{1\times 5+2}{5}$$

Cancel out 9 in both numerator and denominator.

$$\frac{2}{5}-\frac{1\times 5+2}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{2}{5}-\frac{5+2}{5}$$

Add 5 and 2 to get 7.

$$\frac{2}{5}-\frac{7}{5}$$

Since \frac{2}{5} and \frac{7}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-7}{5}$$

Subtract 7 from 2 to get -5.

$$\frac{-5}{5}$$

Divide -5 by 5 to get -1.

$$-1$$

Factor

$$-1$$