Solve frac{frac{1/sqrt{3}}{4sqrt{12}}}{}

$$\frac{ \frac{ \frac{ 1 }{ \sqrt{ 3 } } }{ 4 \sqrt{ 12 } } }{ }$$

Evaluate

$$\frac{1}{24}\approx 0.041666667$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{4\sqrt{12}}}{1}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\frac{\sqrt{3}}{3}}{4\sqrt{12}}}{1}$$

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}.

$$\frac{\frac{\frac{\sqrt{3}}{3}}{4\times 2\sqrt{3}}}{1}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{\frac{\sqrt{3}}{3}}{8\sqrt{3}}}{1}$$

Express \frac{\frac{\sqrt{3}}{3}}{8\sqrt{3}} as a single fraction.

$$\frac{\frac{\sqrt{3}}{3\times 8\sqrt{3}}}{1}$$

Rationalize the denominator of \frac{\sqrt{3}}{3\times 8\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{\sqrt{3}\sqrt{3}}{3\times 8\left(\sqrt{3}\right)^{2}}}{1}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{3}\sqrt{3}}{3\times 8\times 3}}{1}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{\frac{3}{3\times 8\times 3}}{1}$$

Multiply 3 and 8 to get 24.

$$\frac{\frac{3}{24\times 3}}{1}$$

Multiply 24 and 3 to get 72.

$$\frac{\frac{3}{72}}{1}$$

Reduce the fraction \frac{3}{72} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{24}}{1}$$

Anything divided by one gives itself.

$$\frac{1}{24}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3} = 0.041666666666666664$$