Solve sqrt{2*0.01*10^2*1/400}

$$\sqrt{ \frac{ 2 \times 0.01 \times { 10 }^{ 2 } \times 1 }{ 400 } }$$

Evaluate

$$\frac{\sqrt{2}}{20}\approx 0.070710678$$

Solution Steps

Multiply 2 and 0.01 to get 0.02.

$$\sqrt{\frac{0.02\times 10^{2}\times 1}{400}}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{0.02\times 100\times 1}{400}}$$

Multiply 0.02 and 100 to get 2.

$$\sqrt{\frac{2\times 1}{400}}$$

Multiply 2 and 1 to get 2.

$$\sqrt{\frac{2}{400}}$$

Reduce the fraction \frac{2}{400} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{200}}$$

Rewrite the square root of the division \sqrt{\frac{1}{200}} as the division of square roots \frac{\sqrt{1}}{\sqrt{200}}.

$$\frac{\sqrt{1}}{\sqrt{200}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{200}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{1}{10\sqrt{2}}$$

Rationalize the denominator of \frac{1}{10\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{10\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

Multiply 10 and 2 to get 20.

$$\frac{\sqrt{2}}{20}$$