Solve sqrt{{left(1/4right)}^2+{left(2/4right)}^2}

$$\sqrt{ { \left( \frac{ 1 }{ 4 } \right) }^{ 2 } + { \left( \frac{ 2 }{ 4 } \right) }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{5}}{4}\approx 0.559016994$$

Solution Steps

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{\frac{1}{16}+\left(\frac{2}{4}\right)^{2}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{16}+\left(\frac{1}{2}\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\sqrt{\frac{1}{16}+\frac{1}{4}}$$

Add \frac{1}{16} and \frac{1}{4} to get \frac{5}{16}.

$$\sqrt{\frac{5}{16}}$$

Rewrite the square root of the division \sqrt{\frac{5}{16}} as the division of square roots \frac{\sqrt{5}}{\sqrt{16}}.

$$\frac{\sqrt{5}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{5}}{4}$$