Solve 422sqrt{80}*sqrt{5}-sqrt{50}*sqrt{2}

$$422 \sqrt { 80 } \times \sqrt { 5 } - \sqrt { 50 } \times \sqrt { 2 }$$

Evaluate

$$8430$$

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}.

$$422\sqrt{5}\sqrt{16}\sqrt{5}-\sqrt{50}\sqrt{2}$$

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

$$422\times 5\sqrt{16}-\sqrt{50}\sqrt{2}$$

Multiply 422 and 5 to get 2110.

$$2110\sqrt{16}-\sqrt{50}\sqrt{2}$$

Calculate the square root of 16 and get 4.

$$2110\times 4-\sqrt{50}\sqrt{2}$$

Multiply 2110 and 4 to get 8440.

$$8440-\sqrt{50}\sqrt{2}$$

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}.

$$8440-\sqrt{2}\sqrt{25}\sqrt{2}$$

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

$$8440-2\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$8440-2\times 5$$

Multiply 2 and 5 to get 10.

$$8440-10$$

Subtract 10 from 8440 to get 8430.

$$8430$$

Factor

$$2\times 3\times 5\times 281$$