How to square both sides with pythagoras theroem

The theorem is expressed as:

where $a$ and $b$ are the lengths of the two shorter sides (legs), and $c$ is the length of the hypotenuse. Notice that the terms are already squared in the theorem itself.

You would typically "square both sides" of an equation when you need to eliminate a square root to solve for an unknown variable. This often happens when you've rearranged the Pythagorean theorem to solve for one of the sides, and you end up with a square root.

Suppose you have a right triangle where the legs are 3 and 4, and you want to find the hypotenuse $c$.
Using the Pythagorean theorem:

To find $c$, you take the square root of both sides:

Now, consider if you were given $c=5$ and $a=3$, and you needed to find $b$.

To find $b$, you take the square root of both sides:

In these cases, you are taking the square root of both sides to solve for a variable that is squared. The operation of "squaring both sides" would be used if you had an equation like $\sqrt{X} = Y$ and you wanted to find $X$, so you would square both sides to get $X = Y^2$. This is less common directly with the Pythagorean theorem itself, as it's already in squared form.