Give some facts about perfect square .. no spam plx
Answers
FACTS ABOUT PERFECT SQUARE ⤵️
✔️A number ending with an odd number of zeroes (one zero, three zeroes and so is never a perfect square,
e.g. 150, 25000, 350 are not perfect squares.
✔️Squares of even numbers are always even,
e.g.
82 = 64
122 = 144
✔️Squares of odd numbers are always odd, e.g.
72 = 49
132 = 169
202 = 400
212 = 441
✔️The numbers ending with 2, 3, 7, 8 are not perfect squares,
e.g. 32, 243, 37, 368 are not perfect squares.
The square of a number other than 0 and 1, is either a multiple of 3 or exceeds the multiple of 3 by 1.
Examples of multiples of 3.
32 = 9
122 = 144
. Examples of multiples of 3 exceeded by 1.
42 = 16 = (15 + 1)
132 = 169 = (168 + 1)
✔️The square of a number other than 0 and 1, is either a multiple of 4 or exceeds a
multiple of 4 by 1.
Examples of multiples of 4.
6² = 36
8² = 64
Examples of multiples of 4 exceeded by 1.
7² = 49 = (48 + 1)
and no fac
9² = 81 = (80 + 1)
✔️ The difference between the squares of two consecutive natural numbers is equal
to their sum
Let us take two consecutive natural numbers, 3 and 4.
42 - 32 = 16 - 9 = 7 = 4+ 3
Thus, in general, if n and (n + 1) be two consecutive natural numbers,
then (n + 1)² - n = [N + 1) (n +1) - n²
= n² +n+n+ 1- n = n+ (n +1)
✔️The square of a natural number n is equal to the sum of the first n odd natural numbers
e.g. 1²= 1 = sum of the first one odd natural number
2 = 1 + 3 = sum of the first two odd natural numbers
3² = 1+3+5 = sum of the first three odd natural numbers
4² = 1+3+5+ 7 = sum of the first four odd natural numbers
and so on.
✔️squares of natural numbers composed of only digit 1, follow a peculiar pattern.
1² = 1
111² = 12321
1111² = 1234321
11111² = 123454321
Answer:
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Step-by-step explanation:
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