Answer:
[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]
Step-by-step explanation:
We want to simplify the radical expression:
[tex]4 \sqrt{6} \times \sqrt{3} [/tex]
We write √6 as √(2*3).
This implies that:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2 \times 3} \times \sqrt{3} [/tex]
We now split the radical for √(2*3) to get:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times \sqrt{3} \times \sqrt{3} [/tex]
We obtain a perfect square at the far right.
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times (\sqrt{3} )^{2} [/tex]
This simplifies to
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \sqrt{2} \times 3[/tex]
This gives us:
[tex]4 \sqrt{6} \times \sqrt{3} = 4 \times 3 \sqrt{2} [/tex]
and finally, we have:
[tex]4 \sqrt{6} \times \sqrt{3} = 12 \sqrt{2} [/tex]
