Solve sqrt{80}sqrt{5}-sqrt{50}sqrt{2}

$$\sqrt{ 80 } \sqrt{ 5 } - \sqrt{ 50 } \sqrt{ 2 }$$

Evaluate

$$10$$

Solution Steps

Factor 80=5\times 16. Rewrite the square root of the product \sqrt{5\times 16} as the product of square roots \sqrt{5}\sqrt{16}.

$$\sqrt{5}\sqrt{16}\sqrt{5}-\sqrt{50}\sqrt{2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\sqrt{16}-\sqrt{50}\sqrt{2}$$

Calculate the square root of 16 and get 4.

$$5\times 4-\sqrt{50}\sqrt{2}$$

Multiply 5 and 4 to get 20.

$$20-\sqrt{50}\sqrt{2}$$

Factor 50=2\times 25. Rewrite the square root of the product \sqrt{2\times 25} as the product of square roots \sqrt{2}\sqrt{25}.

$$20-\sqrt{2}\sqrt{25}\sqrt{2}$$

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

$$20-2\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$20-2\times 5$$

Multiply 2 and 5 to get 10.

$$20-10$$

Subtract 10 from 20 to get 10.

$$10$$

Factor

$$2\times 5$$