Solve (sqrt{2}+3sqrt{8}-sqrt{50})*2sqrt{2}

$$( \sqrt{ 2 } +3 \sqrt{ 8 } - \sqrt{ 50 } ) \times 2 \sqrt{ 2 }$$

Evaluate

$$8$$

Solution Steps

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}.

$$2\left(\sqrt{2}+3\times 2\sqrt{2}-\sqrt{50}\right)\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$2\left(\sqrt{2}+6\sqrt{2}-\sqrt{50}\right)\sqrt{2}$$

Combine \sqrt{2} and 6\sqrt{2} to get 7\sqrt{2}.

$$2\left(7\sqrt{2}-\sqrt{50}\right)\sqrt{2}$$

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}.

$$2\left(7\sqrt{2}-5\sqrt{2}\right)\sqrt{2}$$

Combine 7\sqrt{2} and -5\sqrt{2} to get 2\sqrt{2}.

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

Multiply 2 and 2 to get 4.

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

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

$$4\times 2$$

Multiply 4 and 2 to get 8.

$$8$$

Factor

$$2^{3}$$