Squares And Cubes 8 Flashcards
A perfect square cannot end in
2,3,7,8
If a no is 5m where m is in the units place and 5 is in the tens place
Then it's square is equal to ((25 + m) x 100) + m sq Eg 56 sq where m is equal to 6 So it's square is (25 + 6) + m = 31 + 36 =3136
(N + 1) sq - n sq is equal to
2n+1
Sum of first n odd nos
N sq
11 sq = 121
111 sq = 12321
1111 sq = 1234321
111111111 sq = 12345678987654321
Just read the unique pattern
Next square number is
M + 2√m + 1
If a perfect square ends in 6 then the digit at the tens place would be
Odd
A perfect square ending in 5 would be followed by
2
In 11 sq sum of digits would be
2 sq and this is a pattern
Is 0 a perfect square
Yep
Digital sum of a number is
The sum of all digits
Digital sum use
It can be used to verify equations that include multiplication.
The digital sum of a perfect square would be
0,1,4,7,9
A perfect square cannot end in
2,3,7,8
11 sq * sum of its digits = 22 sq
111 sq * sum of its digits = 3333 sq
1111 sq * sum of its digits = 4444 sq
Read the pattern
Sum of digits in -
11 sq = 2 sq
111 sq = 3 sq
1111 sq = 4 sq
Read
Squares of numbers greater than one can be expressed by
Either by
3 or 3 plus 1
OR
4 or 4 plus 1
If the number is 5ab then it’s square is
((250 + ab) x 100) + ab sq
If a perfect square ends in 1,4,9 then it’s tens digit will be
Even
No of prime factors of a perfect square is
Odd in number
A perfect square when divided by 3 always leaves remainders
1 or 0
Square of any odd number can be expressed as the sum of
2 consecutive numbers
To know the no of perfect squares present below a number
Take the approximate square root of the number and leave the decimal place
If the number of digits in a perfect square is odd then the number of digits in the square root is
N + 1/ 2 where n stand for the number of digits
Otherwise if it is even then the number of digits is n/2
Square of 105
10 x 11 + 5 sq
Sum of consecutive square numbers is
n(n+1)(2n+1)/6
Square root of 2
1.414
Hardy Ramanujan numbers
1729 , 4104, 13832
Hardy Ramanujam numbers
Numbers expressed as sum of two positive cubes in two different ways
Smallest hardy Ramanujam
1729
