Solve 180/sqrt{12}

$$\frac{ 180 }{ \sqrt{ 12 } }$$

Evaluate

$$30\sqrt{3}\approx 51.961524227$$

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}.

$$\frac{180}{2\sqrt{3}}$$

Rationalize the denominator of \frac{180}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{180\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{180\sqrt{3}}{2\times 3}$$

Cancel out 2\times 3 in both numerator and denominator.

$$30\sqrt{3}$$