Solve sqrt{40}sqrt{50}

$$\sqrt { 40 } \sqrt { 50 }$$

Evaluate

$$20\sqrt{5}\approx 44.72135955$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$2\sqrt{10}\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$2\sqrt{10}\times 5\sqrt{2}$$

Multiply 2 and 5 to get 10.

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

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}.

$$10\sqrt{2}\sqrt{5}\sqrt{2}$$

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

$$10\times 2\sqrt{5}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{5}$$