## SQUARE AND SQUARE ROOTS - ESSENTIAL POINTS

• Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 32 = 3 x 3 = 9 (square of 3 is 9).
• All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.
• Square numbers can only have even number of zeroes at the end.
• Inverse of square is Square Root.
• There are two integral square roots of a perfect square number.
• Positive square root of a number is denoted by the symbol . For example, 42 = 16 gives .
• Perfect Square or Square number: It is the square of some natural number. If m = n2, then m is a perfect square number where m and n are natural numbers. Example: 32 = 3 x 3 = 9
• Properties of Square number:
1. A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
2. A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
3. Square of even numbers are even. Example: 32 = 9, 42 = 16 etc.
4. A number ending in an odd number of zeroes cannot be a perfect square. Example: 10, 1000, 900000, etc.
5. The difference of squares of two consecutive natural number is equal to their sum. (n + 1)2 – n2 = n + 1 + n = 2n + 1.
6. Example: 42 – 32 = 4 + 3 = 7, 122 – 112 = 12 + 11 = 23 etc.
• A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean triplet, if m2 + n2 = p2. Example: 32 + 42 = 9 + 16 = 25 = 52
• Square numbers can only have even number of zeroes at the end.