Solve 3sqrt{12}*sqrt{18}

$$3 \sqrt { 12 } \times \sqrt { 18 }$$

Evaluate

$$18\sqrt{6}\approx 44.09081537$$

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}.

$$3\times 2\sqrt{3}\sqrt{18}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{3}\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$6\sqrt{3}\times 3\sqrt{2}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{3}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$18\sqrt{6}$$