Question

Simplify-

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

Short answer

The value is$12\sqrt{6}+12\sqrt{2}-24\sqrt{3}-24$.

Step-by-step solution

Step 1. Given and explanation

We have$(6-3\sqrt{8})(2\sqrt{6}+\sqrt{8})$.

We will simply multiply the terms and then simplify by combining the like terms to get the value.

Step 2. Multiplying and simplifying the terms.

We have $(6-3\sqrt{8})(2\sqrt{6}+\sqrt{8})$.

Multiplying the terms,

$$\begin{gathered} =(6·2\sqrt{6})+6\sqrt{8}-(3·2\sqrt{48})-(3·8) \\ =12\sqrt{6}+\left(6\sqrt{{\left(2\right)}^2\times 2}\right)-\left(6\sqrt{{\left(4\right)}^2\times 3}\right)-24 \\ =12\sqrt{6}+12\sqrt{2}-24\sqrt{3}-24 \end{gathered}$$
Thus we get the value as$12\sqrt{6}+12\sqrt{2}-24\sqrt{3}-24$.