Square and Square roots

Square and Square roots

We know that a number m is called a square number if it is expressed as n2. Here n is called the square root of m. Square root is the inverse operation of squares. Every square number is a sum of the first n odd natural numbers. A set of three numbers that satisfies the Pythagoras Theorem is called Pythagorean Triplet. Pythagorean Triplets can be found using a general expression (2m)2 + (m2 – 1)2 = (m2 + 1)2, where m is any natural number greater than one. Square root of a given number is a number whose square is equal to the given number. Positive square root of a number is denoted by the symbol √.  Square root of a number can be found using the following three methods: Repeated Subtraction Method Prime Factorisation Method Long Division Method We can find the square root of a given number using Repeated subtraction method: Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero. Count the number of steps it took to get the difference as zero.

To find the square root by prime factorization method: Find the prime factors of the given number. Form pairs of prime factors. Take one prime factor from each pair of prime factors of the given number. Find the product of these prime factors to get the square root of the given number. If prime factors of a number do not occur in pairs, the given number is not a perfect square.