Solve (6sqrt{2}-3sqrt{50}+sqrt{72})*sqrt{2}

$$(6 \sqrt{ 2 } -3 \sqrt{ 50 } + \sqrt{ 72 } ) \times \sqrt{ 2 }$$

Evaluate

$$-6$$

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}.

$$\left(6\sqrt{2}-3\times 5\sqrt{2}+\sqrt{72}\right)\sqrt{2}$$

Multiply -3 and 5 to get -15.

$$\left(6\sqrt{2}-15\sqrt{2}+\sqrt{72}\right)\sqrt{2}$$

Combine 6\sqrt{2} and -15\sqrt{2} to get -9\sqrt{2}.

$$\left(-9\sqrt{2}+\sqrt{72}\right)\sqrt{2}$$

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}.

$$\left(-9\sqrt{2}+6\sqrt{2}\right)\sqrt{2}$$

Combine -9\sqrt{2} and 6\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}\sqrt{2}$$

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

$$-3\times 2$$

Multiply -3 and 2 to get -6.

$$-6$$

Factor

$$-6$$