Solve sqrt{90}*sqrt{72}

$$\sqrt { 90 } \times \sqrt { 72 }$$

Evaluate

$$36\sqrt{5}\approx 80.49844719$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$3\sqrt{10}\sqrt{72}$$

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}.

$$3\sqrt{10}\times 6\sqrt{2}$$

Multiply 3 and 6 to get 18.

$$18\sqrt{10}\sqrt{2}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$18\sqrt{2}\sqrt{5}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$18\times 2\sqrt{5}$$

Multiply 18 and 2 to get 36.

$$36\sqrt{5}$$