Solve 20sqrt{50}*50sqrt{20}

$$20 \sqrt { 50 } \times 50 \sqrt { 20 }$$

Evaluate

$$10000\sqrt{10}\approx 31622.776601684$$

Solution Steps

Multiply 20 and 50 to get 1000.

$$1000\sqrt{50}\sqrt{20}$$

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}.

$$1000\times 5\sqrt{2}\sqrt{20}$$

Multiply 1000 and 5 to get 5000.

$$5000\sqrt{2}\sqrt{20}$$

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}.

$$5000\sqrt{2}\times 2\sqrt{5}$$

Multiply 5000 and 2 to get 10000.

$$10000\sqrt{2}\sqrt{5}$$

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

$$10000\sqrt{10}$$