Solve sqrt{0.01}-sqrt{sqrt{81}}+sqrt{54/9}

$$\sqrt{ 0.01 } - \sqrt{ \sqrt{ 81 } } + \sqrt{ 5 \frac { 4 } { 9 } }$$

Evaluate

$$-\frac{17}{30}\approx -0.566666667$$

Solution Steps

Calculate the square root of 0.01 and get 0.1.

$$0.1-\sqrt{\sqrt{81}}+\sqrt{\frac{5\times 9+4}{9}}$$

Calculate the square root of 81 and get 9.

$$0.1-\sqrt{9}+\sqrt{\frac{5\times 9+4}{9}}$$

Calculate the square root of 9 and get 3.

$$0.1-3+\sqrt{\frac{5\times 9+4}{9}}$$

Subtract 3 from 0.1 to get -2.9.

$$-2.9+\sqrt{\frac{5\times 9+4}{9}}$$

Multiply 5 and 9 to get 45.

$$-2.9+\sqrt{\frac{45+4}{9}}$$

Add 45 and 4 to get 49.

$$-2.9+\sqrt{\frac{49}{9}}$$

Rewrite the square root of the division \frac{49}{9} as the division of square roots \frac{\sqrt{49}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$-2.9+\frac{7}{3}$$

Convert decimal number -2.9 to fraction -\frac{29}{10}.

$$-\frac{29}{10}+\frac{7}{3}$$

Least common multiple of 10 and 3 is 30. Convert -\frac{29}{10} and \frac{7}{3} to fractions with denominator 30.

$$-\frac{87}{30}+\frac{70}{30}$$

Since -\frac{87}{30} and \frac{70}{30} have the same denominator, add them by adding their numerators.

$$\frac{-87+70}{30}$$

Add -87 and 70 to get -17.

$$-\frac{17}{30}$$

Factor

$$-\frac{17}{30} = -0.5666666666666667$$