Short Problem

[Soracyn11]

How would you do this could you show the work?

 

[MarkFL]

If you are to simplify, observe that:

[MATH]4+2\sqrt{3}=(\sqrt{3})^2+2(1)(\sqrt{3})+1^2=(\sqrt{3}+1)^2[/MATH]

 

[Soracyn11]

Thank you.

 

[Steven G]

If you are to simplify, observe that:

[MATH]4+2\sqrt{3}=(\sqrt{3})^2+2(1)(\sqrt{3})+1^2=(\sqrt{3}+1)^2[/MATH]

How do you see these things?

 

[MarkFL]

How do you see these things?

Mainly experience.

 

[Dr.Peterson]

How would you do this could you show the work?

One way to find the answer when you don't just see it is to assume it can be written in the form [MATH]a+b\sqrt{3}[/MATH], with integers (or at least rational numbers) a and b, so that

[MATH](a+b\sqrt{3})^2 = 4+2\sqrt{3}[/MATH]​

Expand the LHS and equate rational and irrational terms, yielding two equations to solve for a and b.

 

[firemath]

Could you show some work?

How would you do this could you show the work?

 

[Steven G]

Could you show some work?

The solution has already been supplied but I do like your post (just a bit late)