Solve sqrt{2*10^-2}*sqrt{2^3*10^-2}

$$\sqrt { 2 \cdot 10 ^ { - 2 } } \cdot \sqrt { 2 ^ { 3 } \cdot 10 ^ { - 2 } }$$

Evaluate

$$\frac{1}{25}=0.04$$

Solution Steps

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\sqrt{2\times \frac{1}{100}}\sqrt{2^{3}\times 10^{-2}}$$

Multiply 2 and \frac{1}{100} to get \frac{1}{50}.

$$\sqrt{\frac{1}{50}}\sqrt{2^{3}\times 10^{-2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{50}} as the division of square roots \frac{\sqrt{1}}{\sqrt{50}}.

$$\frac{\sqrt{1}}{\sqrt{50}}\sqrt{2^{3}\times 10^{-2}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{50}}\sqrt{2^{3}\times 10^{-2}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{1}{5\sqrt{2}}\sqrt{2^{3}\times 10^{-2}}$$

Rationalize the denominator of \frac{1}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}\sqrt{2^{3}\times 10^{-2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{5\times 2}\sqrt{2^{3}\times 10^{-2}}$$

Multiply 5 and 2 to get 10.

$$\frac{\sqrt{2}}{10}\sqrt{2^{3}\times 10^{-2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\sqrt{2}}{10}\sqrt{8\times 10^{-2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\sqrt{2}}{10}\sqrt{8\times \frac{1}{100}}$$

Multiply 8 and \frac{1}{100} to get \frac{2}{25}.

$$\frac{\sqrt{2}}{10}\sqrt{\frac{2}{25}}$$

Rewrite the square root of the division \sqrt{\frac{2}{25}} as the division of square roots \frac{\sqrt{2}}{\sqrt{25}}.

$$\frac{\sqrt{2}}{10}\times \frac{\sqrt{2}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{2}}{10}\times \frac{\sqrt{2}}{5}$$

Multiply \frac{\sqrt{2}}{10} times \frac{\sqrt{2}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{2}\sqrt{2}}{10\times 5}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{2}{50}$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$\frac{1}{25}$$

Factor

$$\frac{1}{5 ^ {2}} = 0.04$$