1. Question 1.
Find the cubes of:
(i) -11
(ii) -12
(iii) – 21
Solution:
(i) (-11)3
=(-11)3
=(11 x 11 x 11) =-1331
(ii) (-12)3
=(-12)3
=(12 x 12 x 12) = -1728
(iii) (-21)3
=(-21)3
=(21 x 21 x 21) = -9261
Question 2.
Which of the following numbers are cubes of negative integers.
(i) -64
(ii) -1056
(iii) -2197
(iv) -2744
(v) -42875
Solution:
∴ All factors of 64 can be grouped in triplets of the equal factors completely.
∴ -64 is a perfect cube of negative integer.
All the factors of 1056 can be grouped in triplets of equal factors grouped completely
∴ 1058 is not a perfect cube of negative integer.
All the factors of -2197 can be grouped in triplets of equal factors completely
2. ∴ 2197 is a perfect cube of negative integer,
All the factors of -2744 can be grouped in triplets of equal factors completely
∴ 2744 is a perfect cube of negative integer
All the factors of -42875 can be grouped in triplets of equal factors completely
∴ 42875 is a perfect cube of negative integer.
Question 3.
Show that the following integers are cubes of negative integers. Also, find the
integer whose cube is the given integer :
(i) -5832 (ii) -2744000
Solution:
Grouping the factors in triplets of equal factors, we see that no factor is left
∴ -5832 is a perfect cube
3. Now taking one factor from each triplet we find that
-5832 is a cube of – (2 x 3 x 3) = -18
∴ Cube root of-5832 = -18
Grouping the factors in tuplets of equal factors, we see that no factor is left.
Therefore it is a perfect cube.
Now taking one factor from each triplet, we find that.
-2744000 is a cube of – (2 x 2 x 5 x 7) ie. -140
∴ Cube root of -2744000 = -140
Question 4.
Find the cube of :
Solution:
4.
5. Question 5.
Which of the following numbers are cubes of rational numbers :
Solution:
