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quares And Squa
- Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4).
- If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number.
- All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place.
- Square numbers can only have even number of zeros at the end.
- Square root is the inverse operation of square.
- There are two integral square roots of a perfect square number.
- Positive square root of a number is denoted by the symbol
For example, 32=9 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: 1=1 x 1=12, 4=2 x 2=22.
- Properties of Square number:
(i) A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
(ii) A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
(iii) Square of even numbers are even. Example: 22 = 4, 42=16 etc.
(iv) Square of odd numbers are odd. Example: 52 = 25, 92 = 81, etc.
(v) A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
(vi) The difference of squares of two consecutive natural number is equal to their sum. (n + 1)2– n2 = n+1+n. Example: 42 – 32 =4 + 3=7. 122– 112 =12+11 =23, etc.
(vii) A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean triplet, if m2 + n2 = p2: 32 + 42 = 25 = 52
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