What are the two square roots of 441 and which is the principal root?
The correct answer and explanation is:
The two square roots of 441 are 21 and -21. Among these, 21 is the principal square root.
Explanation:
A square root is defined as a number that, when multiplied by itself, gives the original number. For example, when looking for the square root of 441, you need to find a number that, when squared (multiplied by itself), results in 441.
Mathematically, if xx is the square root of 441, then x2=441x^2 = 441. Solving for xx, you find that x=21x = 21 because 212=44121^2 = 441. The number -21 is also a square root of 441 because (−21)2=441(-21)^2 = 441, meaning both 21 and -21 satisfy the condition of being square roots of 441.
However, in mathematics, when referring to the square root, the principal square root is typically understood to be the positive value. This is why, when the square root of a number is mentioned without specifying whether it is positive or negative, it refers to the principal square root. Therefore, 21 is considered the principal square root of 441.
This rule applies generally: for any positive number, there are two square roots—one positive and one negative. The principal square root, by convention, is always the positive one. When using the square root symbol (√), it denotes the principal square root. So, for example, √441 refers specifically to 21.
In conclusion, the square roots of 441 are 21 and -21, with 21 being the principal square root.