Solve sqrt{2}(sqrt{50}-sqrt{32})

$$\sqrt { 2 } ( \sqrt { 50 } - \sqrt { 32 } )$$

Evaluate

$$2$$

Solution Steps

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}.

$$\sqrt{2}\left(5\sqrt{2}-\sqrt{32}\right)$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\sqrt{2}\left(5\sqrt{2}-4\sqrt{2}\right)$$

Combine 5\sqrt{2} and -4\sqrt{2} to get \sqrt{2}.

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

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

$$2$$

Factor

$$2$$