Expand and simplify root 6 times (2 - root 7).

Step-by-step solution

1. 1

   Distribute the radical across the bracket. A square root multiplies like any other factor:

   $\sqrt{6}\left(2-\sqrt{7}\right)=\sqrt{6}\cdot 2-\sqrt{6}\cdot\sqrt{7}.$

2. 2

   Handle the rational multiple. The first term is just a coefficient times a surd, conventionally written with the number in front:

   $\sqrt{6}\cdot 2=2\sqrt{6}.$

3. 3

   Combine the two radicals using the product rule. For non-negative $a$ and $b$, $\sqrt{a}\sqrt{b}=\sqrt{ab}$:

   $\sqrt{6}\cdot\sqrt{7}=\sqrt{42}.$

4. 4

   Check whether either surd simplifies further. $6=2\cdot 3$ and $42=2\cdot 3\cdot 7$ — neither contains a repeated prime factor, so neither has a square factor to pull out. Both are already in simplest surd form.

5. 5

   Write the answer and confirm it cannot be combined.

   $2\sqrt{6}-\sqrt{42}.$

   The two terms have different radicands, so they are not like terms and cannot be added. Numerically, $2(2.449490)-6.480741=-1.581761$, and the original $2.449490(2-2.645751)=-1.581761$ — a match to every digit shown.