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

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

Evaluate

$$2\left(\sqrt{3}-12\right)\approx -20.535898385$$

Solution Steps

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

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

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}.

$$\sqrt{2}\sqrt{3}\sqrt{2}-4\left(\sqrt{6}\right)^{2}$$

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

$$2\sqrt{3}-4\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$2\sqrt{3}-4\times 6$$

Multiply -4 and 6 to get -24.

$$2\sqrt{3}-24$$