Solve sqrt{0,04/5}+sqrt[3]{-8}-sqrt{1-16/25}

$$\sqrt { \frac { 0,04 } { 5 } } + \sqrt[ 3 ] { - 8 } - \sqrt { 1 - \frac { 16 } { 25 } }$$

Evaluate

$$\frac{\sqrt{5}}{25}-2,6\approx -2.510557281$$

Short Solution Steps

Expand \frac{0,04}{5} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{4}{500}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Reduce the fraction \frac{4}{500} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{1}{125}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Rewrite the square root of the division \sqrt{\frac{1}{125}} as the division of square roots \frac{\sqrt{1}}{\sqrt{125}}.

$$\frac{\sqrt{1}}{\sqrt{125}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{125}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{1}{5\sqrt{5}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Rationalize the denominator of \frac{1}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{5\left(\sqrt{5}\right)^{2}}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{5\times 5}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Multiply 5 and 5 to get 25.

$$\frac{\sqrt{5}}{25}+\sqrt[3]{-8}-\sqrt{1-\frac{16}{25}}$$

Calculate \sqrt[3]{-8} and get -2.

$$\frac{\sqrt{5}}{25}-2-\sqrt{1-\frac{16}{25}}$$

Subtract \frac{16}{25} from 1 to get \frac{9}{25}.

$$\frac{\sqrt{5}}{25}-2-\sqrt{\frac{9}{25}}$$

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{\sqrt{5}}{25}-2-\frac{3}{5}$$

Subtract \frac{3}{5} from -2 to get -\frac{13}{5}.

$$\frac{\sqrt{5}}{25}-\frac{13}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 5 is 25. Multiply \frac{13}{5} times \frac{5}{5}.

$$\frac{\sqrt{5}}{25}-\frac{13\times 5}{25}$$

Since \frac{\sqrt{5}}{25} and \frac{13\times 5}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{5}-13\times 5}{25}$$

Do the multiplications in \sqrt{5}-13\times 5.

$$\frac{\sqrt{5}-65}{25}$$

Factor

$$\frac{\sqrt{5} - 65}{25} = -2.5105572809000085$$