Solve sqrt{0.01}-sqrt{sqrt{81}}+sqrt{54/9}-sqrt{625}

$$\sqrt{ 0.01 } - \sqrt{ \sqrt{ 81 } } + \sqrt{ 5 \frac { 4 } { 9 } } - \sqrt{ 625 }$$

Evaluate

$$-\frac{767}{30}\approx -25.566666667$$

Solution Steps

Calculate the square root of 0.01 and get 0.1.

$$0.1-\sqrt{\sqrt{81}}+\sqrt{\frac{5\times 9+4}{9}}-\sqrt{625}$$

Calculate the square root of 81 and get 9.

$$0.1-\sqrt{9}+\sqrt{\frac{5\times 9+4}{9}}-\sqrt{625}$$

Calculate the square root of 9 and get 3.

$$0.1-3+\sqrt{\frac{5\times 9+4}{9}}-\sqrt{625}$$

Subtract 3 from 0.1 to get -2.9.

$$-2.9+\sqrt{\frac{5\times 9+4}{9}}-\sqrt{625}$$

Multiply 5 and 9 to get 45.

$$-2.9+\sqrt{\frac{45+4}{9}}-\sqrt{625}$$

Add 45 and 4 to get 49.

$$-2.9+\sqrt{\frac{49}{9}}-\sqrt{625}$$

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.

$$-2.9+\frac{7}{3}-\sqrt{625}$$

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

$$-\frac{29}{10}+\frac{7}{3}-\sqrt{625}$$

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

$$-\frac{87}{30}+\frac{70}{30}-\sqrt{625}$$

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

$$\frac{-87+70}{30}-\sqrt{625}$$

Add -87 and 70 to get -17.

$$-\frac{17}{30}-\sqrt{625}$$

Calculate the square root of 625 and get 25.

$$-\frac{17}{30}-25$$

Convert 25 to fraction \frac{750}{30}.

$$-\frac{17}{30}-\frac{750}{30}$$

Since -\frac{17}{30} and \frac{750}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-750}{30}$$

Subtract 750 from -17 to get -767.

$$-\frac{767}{30}$$

Factor

$$-\frac{767}{30} = -25\frac{17}{30} = -25.566666666666666$$