Solve frac{3sqrt{8}}{4sqrt{12}}

$$\frac { 3 \sqrt { 8 } } { 4 \sqrt { 12 } }$$

Evaluate

$$\frac{\sqrt{6}}{4}\approx 0.612372436$$

Solution Steps

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

$$\frac{3\times 2\sqrt{2}}{4\sqrt{12}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{2}}{4\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{6\sqrt{2}}{4\times 2\sqrt{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{6\sqrt{2}}{8\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{3\sqrt{6}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{3\sqrt{6}}{12}$$

Divide 3\sqrt{6} by 12 to get \frac{1}{4}\sqrt{6}.

$$\frac{1}{4}\sqrt{6}$$