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

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

Evaluate

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

Solution Steps

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}.

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

Multiply 4 and 2 to get 8.

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

Rationalize the denominator of \frac{1}{8\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 8 and 3 to get 24.

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

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

$$\frac{\sqrt{3}}{24}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{3}}{24} times \frac{\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 24 and 3 to get 72.

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

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

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

Factor

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