Solve sqrt{2}(6sqrt{6}-8sqrt{2})

$$\sqrt { 2 } ( 6 \sqrt { 6 } - 8 \sqrt { 2 } )$$

Evaluate

$$4\left(3\sqrt{3}-4\right)\approx 4.784609691$$

Solution Steps

Use the distributive property to multiply \sqrt{2} by 6\sqrt{6}-8\sqrt{2}.

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

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}.

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

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

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

Multiply 6 and 2 to get 12.

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

The square of \sqrt{2} is 2.

$$12\sqrt{3}-8\times 2$$

Multiply -8 and 2 to get -16.

$$12\sqrt{3}-16$$

Factor

$$4 {(3 \sqrt{3} - 4)} = 4.784609691$$