Solve sqrt{72}*2sqrt{80}

$$\sqrt { 72 } \times 2 \sqrt { 80 }$$

Evaluate

$$48\sqrt{10}\approx 151.789327688$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$2\times 6\sqrt{2}\sqrt{80}$$

Multiply 2 and 6 to get 12.

$$12\sqrt{2}\sqrt{80}$$

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}.

$$12\sqrt{2}\times 4\sqrt{5}$$

Multiply 12 and 4 to get 48.

$$48\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$48\sqrt{10}$$