Solve sqrt{0.1^2+0.01^2/4}

$$\sqrt{ { 0.1 }^{ 2 } + \frac{ { 0.01 }^{ 2 } }{ 4 } }$$

Evaluate

$$\frac{\sqrt{401}}{200}\approx 0.100124922$$

Solution Steps

Calculate 0.1 to the power of 2 and get 0.01.

$$\sqrt{0.01+\frac{0.01^{2}}{4}}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$\sqrt{0.01+\frac{0.0001}{4}}$$

Expand \frac{0.0001}{4} by multiplying both numerator and the denominator by 10000.

$$\sqrt{0.01+\frac{1}{40000}}$$

Convert decimal number 0.01 to fraction \frac{1}{100}.

$$\sqrt{\frac{1}{100}+\frac{1}{40000}}$$

Least common multiple of 100 and 40000 is 40000. Convert \frac{1}{100} and \frac{1}{40000} to fractions with denominator 40000.

$$\sqrt{\frac{400}{40000}+\frac{1}{40000}}$$

Since \frac{400}{40000} and \frac{1}{40000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{400+1}{40000}}$$

Add 400 and 1 to get 401.

$$\sqrt{\frac{401}{40000}}$$

Rewrite the square root of the division \sqrt{\frac{401}{40000}} as the division of square roots \frac{\sqrt{401}}{\sqrt{40000}}.

$$\frac{\sqrt{401}}{\sqrt{40000}}$$

Calculate the square root of 40000 and get 200.

$$\frac{\sqrt{401}}{200}$$