Solve sqrt{405}*sqrt{80}

$$\sqrt { 405 } \times \sqrt { 80 }$$

Evaluate

$$180$$

Solution Steps

Factor 405=9^{2}\times 5. Rewrite the square root of the product \sqrt{9^{2}\times 5} as the product of square roots \sqrt{9^{2}}\sqrt{5}. Take the square root of 9^{2}.

$$9\sqrt{5}\sqrt{80}$$

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}.

$$9\sqrt{5}\times 4\sqrt{5}$$

Multiply 9 and 4 to get 36.

$$36\sqrt{5}\sqrt{5}$$

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

$$36\times 5$$

Multiply 36 and 5 to get 180.

$$180$$

Factor

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