Solve 3sqrt{12}*3sqrt{15}

$$3 \sqrt{ 12 } \times 3 \sqrt{ 15 }$$

Evaluate

$$54\sqrt{5}\approx 120.747670785$$

Solution Steps

Multiply 3 and 3 to get 9.

$$9\sqrt{12}\sqrt{15}$$

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}.

$$9\times 2\sqrt{3}\sqrt{15}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{3}\sqrt{15}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$18\sqrt{3}\sqrt{3}\sqrt{5}$$

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

$$18\times 3\sqrt{5}$$

Multiply 18 and 3 to get 54.

$$54\sqrt{5}$$