Solve sqrt{40}divsqrt{5}*sqrt{20}

$$\sqrt { 40 } \div \sqrt { 5 } \times \sqrt { 20 }$$

Evaluate

$$4\sqrt{10}\approx 12.649110641$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{40}}{\sqrt{5}} as the square root of the division \sqrt{\frac{40}{5}} and perform the division.

$$\sqrt{8}\sqrt{20}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

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

$$4\sqrt{10}$$