What is the square root of 196? with explanaition

##sqrt(196)=sqrt(14^2)=14##

The square root of 196 in math symbology looks like this:

##sqrt196##

So what does it mean?

The square root operation is the opposite of squaring something. For instance, 3 squared is 9 and the square root of 9 is 3:

##3^2=9##

##sqrt9=3##

And if I write something like this:

##sqrt(3^2)## that is both operations at once, the square and the square root cancel each other out and the answer is 3:

##sqrt(3^2)=3##

Back to ##sqrt196##. Is there a number we can square to arrive at 196? The answer is yes - 14. There are two ways to figure this out - one is to simply remember it (I used this way because I'm a math geek and I remember stuff like this...) and the other is to work it out by breaking down the 196 into its factors. Like this:

##sqrt196=sqrt(2*98)=sqrt(2*2*49)=sqrt(2*2*7*7)=sqrt(14*14)=sqrt(14^2)##

And now that we know that ##sqrt(196)=sqrt(14^2)##, we can now say:

##sqrt(196)=sqrt(14^2)=14##