Solve 3sqrt{20}*sqrt{45}

$$3 \sqrt { 20 } \times \sqrt { 45 }$$

Evaluate

$$90$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$3\times 2\sqrt{5}\sqrt{45}$$

Multiply 3 and 2 to get 6.

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

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$6\sqrt{5}\times 3\sqrt{5}$$

Multiply 6 and 3 to get 18.

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

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

$$18\times 5$$

Multiply 18 and 5 to get 90.

$$90$$

Factor

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