Could some explain this to me:
sqrt (a^2)
Image attached

Question

Could some explain this to me:
sqrt (a^2)
Image attached

anonymous · Answer

attachment

ranga · Answer

The square root and the square will cancel each other.

anonymous · Answer

If they cancel out, would that just leave a?

anonymous · Answer

it's already assumed that a is positive. If not, the solution is not there because sqrt(a^2) = |a|

anonymous · Answer

Ok. so, why do they cancel eachother out? for future reference.

ranga · Answer

sqrt is same as raising it to the power 1/2

sqrt(a^2) = (a^2)^1/2 = a^(2*1/2) = a^1 = a

anonymous · Answer

wow. awesome, thanks so much. That's just what I need to have explained.

ranga · Answer

you are welcome.

parthkohli · Answer

Uh, a would be the most appropriate here, but isn't |a| correct?
For example, sqrt[(-3)^2] is not -3.

anonymous · Answer

I agree with people saying sqrt(a^2)=|a|

ranga · Answer

Yes, it is but have to go with the given choices to answer this problem.

anonymous · Answer

All the choices are wrong if there is no restriction on a. The person who asked this question should be responsible. In Math, you do not assume that something is >0 is if it is not given.

kc_kennylau · Answer

Well, the square root of a number(a) is another number(b) that forms the original number(a) when multiplied to itself(b), that is "for all a, sqrt(a)=b --> b^2=a"