Solve sqrt{2}(sqrt{8}-sqrt{72})

$$\sqrt { 2 } ( \sqrt { 8 } - \sqrt { 72 } )$$

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}.

$$\sqrt{2}\left(2\sqrt{2}-\sqrt{72}\right)$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Combine 2\sqrt{2} and -6\sqrt{2} to get -4\sqrt{2}.

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

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

$$2\left(-4\right)$$

Multiply 2 and -4 to get -8.

$$-8$$

Factor

$$-8$$