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

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

Evaluate

$$2\left(\sqrt{5}-4\sqrt{3}\right)\approx -9.384270506$$

Solution Steps

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

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

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}.

$$\sqrt{2}\sqrt{2}\sqrt{5}-4\sqrt{2}\sqrt{6}$$

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

$$2\sqrt{5}-4\sqrt{2}\sqrt{6}$$

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}.

$$2\sqrt{5}-4\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$2\sqrt{5}-4\times 2\sqrt{3}$$

Multiply -4 and 2 to get -8.

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