Solve 4sqrt{45}*sqrt{80}

$$4 \sqrt { 45 } \times \sqrt { 80 }$$

Evaluate

$$240$$

Solution Steps

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}.

$$4\times 3\sqrt{5}\sqrt{80}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{5}\sqrt{80}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$12\sqrt{5}\times 4\sqrt{5}$$

Multiply 12 and 4 to get 48.

$$48\sqrt{5}\sqrt{5}$$

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

$$48\times 5$$

Multiply 48 and 5 to get 240.

$$240$$

Factor

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