Squares And Square Roots | Study

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. (Scroll down to continue …)

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:

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: 2² = 4, 4²=16 etc.
4. Square of odd numbers are odd. Example: 5² = 25, 9² = 81, etc.
5. A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
6. 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.
7. 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