What is the square root of a square?

Answer 1

√(a^2)

That is |a| (the absolute value of a)

Because if a is positive, a^2 is positive, and since √ is a positive square root, √(a^2) is a.

If a is negative, a^2 is positive, and since √ is a positive square root, √(a^2) is -a.

So if a is positive, √(a^2) is positive (which is a)

If a is negative, √(a^2) is also positive (which is -a)

So √(a^2) is |a| for every a.