Solve frac{(sqrt{8})^2}{(4sqrt{2})^2}=

$$\frac { ( \sqrt { 8 } ) ^ { 2 } } { ( 4 \sqrt { 2 } ) ^ { 2 } } =$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

The square of \sqrt{8} is 8.

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

Expand \left(4\sqrt{2}\right)^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$\frac{8}{16\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{8}{16\times 2}$$

Multiply 16 and 2 to get 32.

$$\frac{8}{32}$$

Reduce the fraction \frac{8}{32} to lowest terms by extracting and canceling out 8.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$