Solve 2sqrt{6}(-3sqrt{2}+4sqrt{6})

$$2 \sqrt { 6 } ( - 3 \sqrt { 2 } + 4 \sqrt { 6 } )$$

Evaluate

$$48-12\sqrt{3}\approx 27.215390309$$

Solution Steps

Use the distributive property to multiply 2\sqrt{6} by -3\sqrt{2}+4\sqrt{6}.

$$-6\sqrt{6}\sqrt{2}+8\left(\sqrt{6}\right)^{2}$$

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}.

$$-6\sqrt{2}\sqrt{3}\sqrt{2}+8\left(\sqrt{6}\right)^{2}$$

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

$$-6\times 2\sqrt{3}+8\left(\sqrt{6}\right)^{2}$$

Multiply -6 and 2 to get -12.

$$-12\sqrt{3}+8\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$-12\sqrt{3}+8\times 6$$

Multiply 8 and 6 to get 48.

$$-12\sqrt{3}+48$$