Solve sqrt{6}*sqrt{45}*sqrt{30}

$$\sqrt { 6 } \times \sqrt { 45 } \times \sqrt { 30 }$$

Evaluate

$$90$$

Solution Steps

Factor 30=6\times 5. Rewrite the square root of the product \sqrt{6\times 5} as the product of square roots \sqrt{6}\sqrt{5}.

$$\sqrt{6}\sqrt{45}\sqrt{6}\sqrt{5}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$6\sqrt{45}\sqrt{5}$$

Factor 45=5\times 9. Rewrite the square root of the product \sqrt{5\times 9} as the product of square roots \sqrt{5}\sqrt{9}.

$$6\sqrt{5}\sqrt{9}\sqrt{5}$$

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

$$6\times 5\sqrt{9}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$30\times 3$$

Multiply 30 and 3 to get 90.

$$90$$

Factor

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