Solve 2sqrt{3}*3sqrt{15}*4sqrt{5}

$$2 \sqrt{ 3 } \times 3 \sqrt{ 15 } \times 4 \sqrt{ 5 }$$

Evaluate

$$360$$

Solution Steps

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}.

$$2\times 3\times 4\sqrt{3}\sqrt{3}\sqrt{5}\sqrt{5}$$

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

$$2\times 3\times 4\times 3\sqrt{5}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\times 3\times 4\times 3\times 5$$

Multiply 2 and 3 to get 6.

$$6\times 4\times 3\times 5$$

Multiply 6 and 4 to get 24.

$$24\times 3\times 5$$

Multiply 24 and 3 to get 72.

$$72\times 5$$

Multiply 72 and 5 to get 360.

$$360$$

Factor

$$2^{3}\times 3^{2}\times 5$$