Square and Cube of Number:-
Square of Number:-square of a any number is multiply it by itself,
As 3 × 3 = 9
It is also written as 32=9.
Short trick for finding square of any number :-
As we know that
(1) (a+b)2 = a2+2ab +b2.
As 3 × 3× 3 =27
It is also written as 33=27.
Short trick for finding cube of any number :-
As we know that
(1) (a+b)3 = a3+3a2b +3ab2+b3.
233=(20+3)3 =203+3*202*3+ 3*20*32 +33.
Square of Number:-square of a any number is multiply it by itself,
As 3 × 3 = 9
It is also written as 32=9.
Short trick for finding square of any number :-
As we know that
(1) (a+b)2 = a2+2ab +b2.
232=(20+3)2
=202+2*20*3 +32.
=
400 + 120 +9
= 400
+ 120
+ 9
529
(2) (a+b)2 = a2 2ab b2. where a is first digit and b is second digit.
At the time of adding take single digit of 2ab and b2 If there is second
or third digit take carry and add it to previous digit.
or third digit take carry and add it to previous digit.
Example 1.:- 232=(2+3)2 = 22 2*2*3 32.
= 4 12 9
+ 1 carry -- 9
5 12 9
529
Ans. is 529
Example 2.:- 1222=(12+2)2 = 122 2*12*2 22.
= 144 48 4
+ 4(carry) ---- ---
148 48 4
14884
Ans. is 14884
Example 3.:- 1392=(13+9)2 = 132 2*13*9 92.
= 169 234 81
+24 carry 8 carry ==
193 242 81
19321
Ans. is 19321.
Cube of Number:-Cube of a any number is multiply it by twice itself,As 3 × 3× 3 =27
It is also written as 33=27.
Short trick for finding cube of any number :-
As we know that
(1) (a+b)3 = a3+3a2b +3ab2+b3.
233=(20+3)3 =203+3*202*3+ 3*20*32 +33.
= 8000 + 3600 +540+27
=
+
+
+ 27
12167
Ans. is 12167.
(2) (a+b)3 = a3 3a2b 3ab2 b3.
where a is first digit and b is second digit.
At the time of adding take single digit of 3a2b,3ab2 and b3
If there is second or third digit take carry and add it to previous digit.
Example 1.:- 233=(2+3)3 =23 3*22*3 3*2*32 33.
(2) (a+b)3 = a3 3a2b 3ab2 b3.
where a is first digit and b is second digit.
At the time of adding take single digit of 3a2b,3ab2 and b3
If there is second or third digit take carry and add it to previous digit.
Example 1.:- 233=(2+3)3 =23 3*22*3 3*2*32 33.
= 8 36 54 27
4 5 2 --
12 41 56 27
12167
Ans. is 12167.
Example 2.:-
Example 2.:-
1213=(12+1)3 =123 3*122*1 3*12*12 13.
= 1728 432 36 1
43 3 -- --
1771 435 36 1
1771561
Ans. is 1771561.
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