Just as subtraction is the inverse operation of addition and division is the inverse operation of multiplication, the square root operation is the inverse of the squaring operation.
Algebraically, you can see the analogues between operations and their inverses:
Addition solves problems like 6 + 7 = x, while subtraction solves problems like 6 + x = 7
Multiplication solves problems like 7 * 5 = x, while division solves problems like 5x = 7
Squaring solves problems like 2^2 = x, while square rooting solves problems like x^2 = 2