Finding Square Root and Representation of Square Root

Square means when a number is multiplied by itself, the product is the square of that number. That is, in general, if a is any number,

a x a = a²

Example: 2 x 2 = 4. Hence 4 is the square of 2 or 2 squared is 4.

Conversely, we can say that a² is the product when ‘a’ is multiplied by itself and in such a case we call a is the square root of a². This leads to the definition of a square root.

The square root of any number is that factor when multiplied by itself leads to the given number as the answer.

Square root formula

The symbol used to denote a square root is ‘√ ‘. It is also called as radical sign. If a is the square root of a, then it is symbolically represented as

a = √n (formula in surd form}

Like we use 2 as the exponent to denote a square, ½ is used as exponent to express a square root. That is the same representation can also be expressed as

a = n^½ (formula in exponential form)

Representation of square roots in exponential form helps in algebraic operation with square roots. We will study more on this at a later stage.

Remember that when a negative number is multiplied by itself, the product is positive. Therefore, the square root of a positive number could either be positive or negative. But no number when multiplied by itself can give the product as a negative number. Therefore, square root of a negative number does not exist.