What is the square root in math?

Answer 1

The square root of a number which when multiplied by itself gives the original number.

eg √4 = 2 since 2 × 2 = 4.

As a negative times a negative is positive, there are two square roots for every positive number: 2 × 2 = -2 × -2 = 4 so both 2 and -2 as the square roots of 4. Also, negative numbers do not have square roots (that are real numbers*)

By convention/definition the radical symbol (√) is used to denote the positive square root.

* Negative numbers have square roots that are complex numbers. These numbers have a real bit and an imaginary bit, and are of the form (a + bi) where a and b are real numbers and i is used to denote the square root of -1 (except in electrical engineering where the little 'i' is used to denote small currents so the little 'j' is used instead); thus: i² = -1.

eg √-4 = √(4 × -1) = √4 √-1 = 2 √-1 = 2i

squaring: (2i)² = 2² × i² = 4 × -1 = -4.