Solve frac{sqrt{27}sqrt{12}}{sqrt{3}}

$$\frac{ \sqrt{ 27 } \sqrt{ 12 } }{ \sqrt{ 3 } }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

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}.

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

Multiply 3 and 2 to get 6.

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

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

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

Multiply 6 and 3 to get 18.

$$\frac{18}{\sqrt{3}}$$

Rationalize the denominator of \frac{18}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{18\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{18\sqrt{3}}{3}$$

Divide 18\sqrt{3} by 3 to get 6\sqrt{3}.

$$6\sqrt{3}$$