How do I find the square root of 196? With a detailed explanation?

1 Answer

Answer:

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

Explanation:

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#