Solve frac{sqrt{2}+4}{4sqrt{2}}

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

Evaluate

$$\frac{\sqrt{2}}{2}+\frac{1}{4}\approx 0.957106781$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}+4}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$\frac{\left(\sqrt{2}+4\right)\sqrt{2}}{8}$$

Use the distributive property to multiply \sqrt{2}+4 by \sqrt{2}.

$$\frac{\left(\sqrt{2}\right)^{2}+4\sqrt{2}}{8}$$

The square of \sqrt{2} is 2.

$$\frac{2+4\sqrt{2}}{8}$$