I need some one to explain me how to simplify radicals.

Question

anonymous · Answer

$$-12\sqrt{12}$$

parthkohli · Answer

$ \color{Black}{\Rightarrow -12\sqrt{3 \times 2 \times 2} }$

$ \color{Black}{\Rightarrow -12\sqrt{3 \times 2^2} }$

$ \color{Black}{\Rightarrow -12\sqrt{3} \times \sqrt{2^2} }$

$ \color{Black}{\Rightarrow -12\sqrt3 \times 2 }$

$ \color{Black}{\Rightarrow -24\sqrt3 }$

jackellyn · Answer

Like @ParthKohli did, if you can factor the number inside the radical, then do so. Any repeated numbers (twice repeated) can be taken out and multiplied by the -12. Any numbers left over are multiplied and stay inside the radical.

anonymous · Answer

where does the -24 come from?

parthkohli · Answer

Okay, I'll explain. What is $-12 \times \sqrt{3} \times 2$?

anonymous · Answer

-12[\sqrt{6}\]

parthkohli · Answer

nope... the 2 is not inside the radical

jackellyn · Answer

Only numbers in radicals can be multiplied together.

anonymous · Answer

then I don't know

parthkohli · Answer

$ \color{Black}{\Rightarrow -12 \times 2 \times \sqrt3 }$
Commutative property ^

$ \color{Black}{\Rightarrow (-12 \times 2) \times \sqrt{3} }$
^ Associative property.

$ \color{Black}{\Rightarrow -24\sqrt3 }$

anonymous · Answer

Oh, I see now.

anonymous · Answer

Thank you