Solve -sqrt{2}(sqrt{10}-4sqrt{6})

$$- \sqrt { 2 } ( \sqrt { 10 } - 4 \sqrt { 6 } )$$

Evaluate

$$8\sqrt{3}-2\sqrt{5}\approx 9.384270506$$

Solution Steps

Use the distributive property to multiply -\sqrt{2} by \sqrt{10}-4\sqrt{6}.

$$\left(-\sqrt{2}\right)\sqrt{10}-4\left(-\sqrt{2}\right)\sqrt{6}$$

Multiply -4 and -1 to get 4.

$$\left(-\sqrt{2}\right)\sqrt{10}+4\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\left(-\sqrt{2}\right)\sqrt{10}+4\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$\left(-\sqrt{2}\right)\sqrt{10}+4\times 2\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$\left(-\sqrt{2}\right)\sqrt{10}+8\sqrt{3}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$-\sqrt{2}\sqrt{2}\sqrt{5}+8\sqrt{3}$$

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

$$-2\sqrt{5}+8\sqrt{3}$$