Solve frac{3sqrt{132}}{sqrt{128}}

$$\frac { 3 \sqrt { 132 } } { \sqrt { 128 } }$$

Evaluate

$$\frac{3\sqrt{66}}{8}\approx 3.046514402$$

Solution Steps

Factor 132=2^{2}\times 33. Rewrite the square root of the product \sqrt{2^{2}\times 33} as the product of square roots \sqrt{2^{2}}\sqrt{33}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{33}}{\sqrt{128}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{33}}{\sqrt{128}}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{6\sqrt{33}}{8\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{33}}{4\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{33}}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{33}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{33}\sqrt{2}}{4\times 2}$$

To multiply \sqrt{33} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{66}}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{3\sqrt{66}}{8}$$