Solve sqrt{12}*sqrt{27}

$$\sqrt { 12 } \times \sqrt { 27 }$$

Evaluate

$$18$$

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}.

$$2\sqrt{3}\sqrt{27}$$

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}.

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

Multiply 2 and 3 to get 6.

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

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

$$6\times 3$$

Multiply 6 and 3 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$