Solve 785/14sqrt{12}

$$\frac{ 785 }{ 14 \sqrt{ 12 } }$$

Evaluate

$$\frac{785\sqrt{3}}{84}\approx 16.18642719$$

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}.

$$\frac{785}{14\times 2\sqrt{3}}$$

Multiply 14 and 2 to get 28.

$$\frac{785}{28\sqrt{3}}$$

Rationalize the denominator of \frac{785}{28\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{785\sqrt{3}}{28\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{785\sqrt{3}}{28\times 3}$$

Multiply 28 and 3 to get 84.

$$\frac{785\sqrt{3}}{84}$$