Square root, Cube root, Surds and Indices

Characteristics of square numbers


1. A square cannot end with an odd number of zeros
2. A square cannot end with an odd number 2, 3, 7 or 8
3. The square of an odd number is odd
4. The square of an even number is even.
5. Every square number is a multiple of 3 or exceeds a multiple of 3 by unity.
Ex.
4 × 4 = 16 = 5 × 3 + 1
5 × 5 = 25 = 8 × 3 + 1
7 × 7 = 49 = 16 × 3 + 1
6. Every square number is a multiple of 4 or exceeds a multiple of 4 by unity.
Ex.
5 × 5 = 25 = 6 × 4 + 1
7 × 7 = 49 = 12 × 4 + 1
7. If a square numbers ends in ‘9’, the preceding digit is even.
Ex.
7 × 7 = 49 ‘4’ is the preceding even numbers
27 × 27 = 729 ‘2’ is the preceding even numbers.
Characteristics of square roots of numbers
1. If a square number ends in ‘9’, its square root is a number ending in’3’ or ‘7’.
2. If a square number ends in ‘1’, its square root is a number ending in’1’ or ‘9’.
3. If a square number ends in ‘5’, its square root is a number ending in’5’
4. If a square number ends in ‘4’, its square root is a number ending in’2’ or ‘8’.
5. If a square number ends in ‘6’, its square root is a number ending in’4’ or ‘6’.
6. If a square number ends in ‘0’, its square root is a number ending in ‘0’.

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