Cube and Cube Root
Points to Remember:
1.
If a number is multiplied by itself thrice
then the product obtained is cube of the number. Let a number be ‘a’ then cube
of a = a x a x a which is written as a3 and read as cube of a.
2.
1, 8, 27 ….. 1000 are perfect cubes.
3.
Cube of an odd number is odd.
4.
Cube of an even number is even.
5.
Cube of positive number is positive.
6.
Cube of negative number is negative.
7.
If unit’s place digits of a number is 1, 4,
5, 6, 9 and 0 then unit’s place digit of its cube is 1, 4, 5, 6, 9 and 0
respectively.
8.
If unit’s place digit of a number is 2 then
unit’s place digit of its cube is 8.
9.
If unit’s place digit of a number is 8 then
unit’s place digit of its cube is 2.
10. If
unit’s place digit of a number is 3 then unit’s place digit of its
cube is 7.
11. If
unit’s place digit of a number is 7 then unit’s place digit of its
cube is 3.
Points to Remember:
1. If
the cube of a number m = m3 = n then cube root of n is m and we will write 3Ön = m.
2. To
find the cube of a number, we add 1+ (n) (n – 1) x 3 in the previous cube ;
when n = 1, 2, 3 …… etc.
e.g. for n = 1, 1 + (1) (1 – 1) x 3 =1
for n = 2, 1 + (2) (2 – 1) x 3 =7
for n = 3, 1 + (3) (3 – 1) x 3 =19
for n = 4, 1 + (4) (4 – 1) x 3 =37
(
………………………………….)
For n = 9, 1 + (9) (9 - 1) x 3 = 217
Thus
by adding 1, 7, 19, 37, 61 ………… 217 etc, to the previous cube, the next cube is
obtained.
3. If by subtracting above numbers i.e. 1, 7,
19, 37, 61, 91, 169, 217,
271 etc. in order from the given number,
the remainder is zero, then
the number is perfect cube otherwise it
is not a perfect cube.
Points to Remember:
1.
The
numbers having unit’s place digit
(i) 0, 1, 4, 5, 6 and 9 then their cubes have
unit’s place digit as 0,
1, 4, 5, 6 and respectively.
(ii) 2, then unit’s place digit of its cube is 8
(iii)
8, then unit’s place digit of its cube is 2
(iv)
3, then unit’s place digit of its cube is 7
(v) 7, then unit’s place digit of its cube is 3
Therefore, the unit’s place digit of
cube root of a number is known by the unit’s place digit of the number.
2. (i) Cube of one digit
number has maximum three digits.
(ii) Cube of two
digit number has maximum six digits.
Points to Remember:
1. Cube of a negative number is negative and cube root of a
negative number is also negative 3Ö-m=-3Öm
2. For
a rational number p, 3Öp =3Öp
q
q Öq
3. If
there are two numbers a and b then 3Ö a x b = 3Ö a x 3Öb
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