Solve sqrt[3]{0.008}*sqrt{19/16}+sqrt{5^2}divsqrt[3]{-1/125}

$$\sqrt[ 3 ] { 0.008 } \times \sqrt { 1 \frac { 9 } { 16 } } + \sqrt { 5 ^ { 2 } } \div \sqrt[ 3 ] { - \frac { 1 } { 125 } }$$

Evaluate

$$-24.75$$

Solution Steps

Calculate \sqrt[3]{0.008} and get \frac{1}{5}.

$$\frac{1}{5}\sqrt{\frac{1\times 16+9}{16}}+\frac{\sqrt{5^{2}}}{\sqrt[3]{-\frac{1}{125}}}$$

Multiply 1 and 16 to get 16.

$$\frac{1}{5}\sqrt{\frac{16+9}{16}}+\frac{\sqrt{5^{2}}}{\sqrt[3]{-\frac{1}{125}}}$$

Add 16 and 9 to get 25.

$$\frac{1}{5}\sqrt{\frac{25}{16}}+\frac{\sqrt{5^{2}}}{\sqrt[3]{-\frac{1}{125}}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{5}\times \frac{5}{4}+\frac{\sqrt{5^{2}}}{\sqrt[3]{-\frac{1}{125}}}$$

Multiply \frac{1}{5} and \frac{5}{4} to get \frac{1}{4}.

$$\frac{1}{4}+\frac{\sqrt{5^{2}}}{\sqrt[3]{-\frac{1}{125}}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1}{4}+\frac{\sqrt{25}}{\sqrt[3]{-\frac{1}{125}}}$$

Calculate the square root of 25 and get 5.

$$\frac{1}{4}+\frac{5}{\sqrt[3]{-\frac{1}{125}}}$$

Calculate \sqrt[3]{-\frac{1}{125}} and get -\frac{1}{5}.

$$\frac{1}{4}+\frac{5}{-\frac{1}{5}}$$

Divide 5 by -\frac{1}{5} by multiplying 5 by the reciprocal of -\frac{1}{5}.

$$\frac{1}{4}+5\left(-5\right)$$

Multiply 5 and -5 to get -25.

$$\frac{1}{4}-25$$

Subtract 25 from \frac{1}{4} to get -\frac{99}{4}.

$$-\frac{99}{4}$$

Factor

$$-24.75$$