Finding the square root of a big number, like 676? I am having trouble understanding and finding the square roots of large numbers. How would I go about finding this number efficiently?

Square root of $676$ is the number such that multiplied by itself will give you 676.
This number is denoted as $\sqrt{676}$.
Note that generally speaking, for a non-zero real number  $p$ there are two numbers which squared will give you $p$. They differ by the sign. In order to ensure uniqueness of the square root, the general convention is for positive numbers to denote square  another positive number as its square root.
If you want to calculate a square root of a large number, it is often helpful to represent this large number as a product of smaller numbers, e.g.
$$
676 = 4\cdot 169 = (2\cdot 2) \cdot (13\cdot 13) = 2^2\cdot 13^2
$$
Therefore 
$$
\sqrt{676} = \sqrt{4\cdot 169 }  = \sqrt{2^2}\cdot \sqrt{ 13^2} =  26
$$

EDIT: 
Thanks to the comments, I am able to get rid of unclarity in my original post.
