Question

Help me with this question

Answer 1

First we simplify $\sqrt{12}$ :

$\sqrt{12}$ = $\sqrt{4}$ × $\sqrt{3}$

This can be simplified further, because $\sqrt{4}$ is just 2:

$\sqrt{4}$ × $\sqrt{3}$ = 2$\sqrt{3}$

So $\sqrt{12}$ = 2$\sqrt{3}$

----------------------------

Now we write 2$\sqrt{3}$ instead of $\sqrt{12}$ in the question:

2$\sqrt{3}$ ( -1 + $\sqrt{5}$)  

We solve this by multiplying 2$\sqrt{3}$ by the numbers in the brackets:

2$\sqrt{3}$ ( -1 + $\sqrt{5}$) = -2$\sqrt{3}$ + 2$\sqrt{15}$

(Explanation: 2$\sqrt{3}$ × -1 = -2$\sqrt{3}$ ,  and 2$\sqrt{3}$ × $\sqrt{5}$ = 2$\sqrt{15}$  because the numbers inside of the squares are multiplied by each other - So the 3 times the 5 equals 15)

-----------------

Answer:

-2$\sqrt{3}$ + 2$\sqrt{15}$

 (Option B)