Solve sqrt{2/25}*sqrt{1/2}+sqrt[3]{8/125}-left(3*2right)^2

$$\sqrt{ \frac{ 2 }{ 25 } } \times \sqrt{ \frac{ 1 }{ 2 } } + \sqrt[ 3 ]{ \frac{ 8 }{ 125 } } - { \left(3 \cdot 2 \right) }^{ 2 }$$

Evaluate

$$-\frac{177}{5}=-35.4$$

Solution Steps

To multiply \sqrt{\frac{2}{25}} and \sqrt{\frac{1}{2}}, multiply the numbers under the square root.

$$\sqrt{\frac{1}{25}}+\sqrt[3]{\frac{8}{125}}-\left(3\times 2\right)^{2}$$

Rewrite the square root of the division \frac{1}{25} as the division of square roots \frac{\sqrt{1}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{1}{5}+\sqrt[3]{\frac{8}{125}}-\left(3\times 2\right)^{2}$$

Calculate \sqrt[3]{\frac{8}{125}} and get \frac{2}{5}.

$$\frac{1}{5}+\frac{2}{5}-\left(3\times 2\right)^{2}$$

Add \frac{1}{5} and \frac{2}{5} to get \frac{3}{5}.

$$\frac{3}{5}-\left(3\times 2\right)^{2}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{5}-6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{3}{5}-36$$

Subtract 36 from \frac{3}{5} to get -\frac{177}{5}.

$$-\frac{177}{5}$$

Factor

$$-\frac{177}{5} = -35\frac{2}{5} = -35.4$$