Solve sqrt{20*10^-2}*888*10^-12

$$\sqrt{ 20 \times { 10 }^{ -2 } } \times 888 \times { 10 }^{ -12 }$$

Evaluate

$$\frac{111\sqrt{5}}{625000000000}\approx 3.971256728 \cdot 10^{-10}$$

Solution Steps

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

$$888\sqrt{20\times \frac{1}{100}}\times 10^{-12}$$

Multiply 20 and \frac{1}{100} to get \frac{1}{5}.

$$888\sqrt{\frac{1}{5}}\times 10^{-12}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$888\times \frac{\sqrt{1}}{\sqrt{5}}\times 10^{-12}$$

Calculate the square root of 1 and get 1.

$$888\times \frac{1}{\sqrt{5}}\times 10^{-12}$$

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

$$888\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times 10^{-12}$$

The square of \sqrt{5} is 5.

$$888\times \frac{\sqrt{5}}{5}\times 10^{-12}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$888\times \frac{\sqrt{5}}{5}\times \frac{1}{1000000000000}$$

Multiply 888 and \frac{1}{1000000000000} to get \frac{111}{125000000000}.

$$\frac{111}{125000000000}\times \frac{\sqrt{5}}{5}$$

Multiply \frac{111}{125000000000} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{111\sqrt{5}}{125000000000\times 5}$$

Multiply 125000000000 and 5 to get 625000000000.

$$\frac{111\sqrt{5}}{625000000000}$$