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

$\sqrt{196} = \sqrt{{14}^{2}} = 14$

Explanation:

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

$\sqrt{196}$

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:

${3}^{2} = 9$

$\sqrt{9} = 3$

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 $\sqrt{196}$. 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:

$\sqrt{196} = \sqrt{2 \cdot 98} = \sqrt{2 \cdot 2 \cdot 49} = \sqrt{2 \cdot 2 \cdot 7 \cdot 7} = \sqrt{14 \cdot 14} = \sqrt{{14}^{2}}$

And now that we know that $\sqrt{196} = \sqrt{{14}^{2}}$, we can now say:

$\sqrt{196} = \sqrt{{14}^{2}} = 14$