Question

6root3+5root12 = ?
What is the answer??

Answer 1

6root3+5root4×3

6root3+5×2root3

6root3+10root3

16root3

Answer 2

$6\sqrt{3} + 5 \sqrt{12}$

In order to add these together, we must simplify the square roots.

$6 \sqrt{3}$ is already in simplest terms, but $5\sqrt{12}$ is not.

So, let's start simplifying it.

$\sqrt{12} = ?$

We need to take out any squares within 12.

So, if we branch out 12, we know that 4 $\times$ 3 = 12

$\sqrt{4}$ = 2. So, we can take out 2 and be left with $\sqrt{3}$.

Since the original square is $5\sqrt{12}$, we MUST multiply 5 by 2.

$5\times2 \sqrt{3} = 10 \sqrt{3}$  

So, using the simplified number of 5 root 12, we now can add this to 6 root 3.  

$6 \sqrt{3} + 10 \sqrt{3} = 16 \sqrt{3}$

So, the final answer is: $16 \sqrt{3}$