Question

4√6 •√3 how do I show work for this because the answer is 2√12​

Answer 1

Answer:

$4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2}$

Step-by-step explanation:

We want to simplify the radical expression:

$4 \sqrt{6} \times \sqrt{3}$

We write √6 as √(2*3).

This implies that:

$4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2 \times 3} \times \sqrt{3}$

We now split the radical for √(2*3) to get:

$4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times \sqrt{3} \times \sqrt{3}$

We obtain a perfect square at the far right.

$4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times (\sqrt{3} )^{2}$

This simplifies to

$4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times 3$

This gives us:

$4 \sqrt{6} \times \sqrt{3} = 4 \times 3 \sqrt{2}$

and finally, we have:

$4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2}$