Find the cube of 12 by using 'sutra Nikhilam'.
Answers
Step-by-step explanation:
By Nikhilam sutra, cube=s
2
(No.+2d)/s×3d
2
/d
3
where s=sub-base, d=difference
(i) 103
base=100;
sub-base=[103/100]=1
d=103−(100×1)=3
Cube=1
2
(103+2(3))/1×3(3
2
)/3
3
As base is 100, we'll take two digits 109/27/27
1092727
(ii) 105
base=100; sub-base=[105/100]=1
d=105−100×1=5
Cube=105+2(5)/3(5
2
)/5
3
=115/75/125
=1157625
(iii) 107
base=100; sub-base=[107/100]=1
d=107−(100×1)=7
Cube=107+2(7)/3(7
2
)/7
3
=121/147/343
=1225043.
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Nikhilam sutra ,
base = 10 , deviation = +2
so,
cube of no. = no. + ( deviatiyon × 2 ) / 3 × deviation²/ deviation ³
cube of no. = 12 + ( 2 × 2 ) /3 × (2)²/(2)³
cube of no. = 12 + 4/3 × 4 /8
cube of no. = 16/12/8 ( sending 1 to 6 = 7 )
7
cube of no = 1728 .