RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2

Other Exercises

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:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 1

∴ All factors of 64 can be grouped in triplets of the equal factors completely.
∴ -64 is a perfect cube of negative integer.
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 2
All the factors of 1056 can be grouped in triplets of equal factors grouped completely
∴ 1058 is not a perfect cube of negative integer.
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 3
All the factors of -2197 can be grouped in triplets of equal factors completely
∴ 2197 is a perfect cube of negative integer,
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 4
All the factors of -2744 can be grouped in triplets of equal factors completely
∴ 2744 is a perfect cube of negative integer
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 5
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:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 6
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 7
Grouping the factors in triplets of equal factors, we see that no factor is left
∴ -5832 is a perfect cube
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
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 8
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 :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 9
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 10
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 11

Question 5.
Which of the following numbers are cubes of rational numbers :
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 12
Solution:
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 13
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 14
RD Sharma Class 8 Solutions Chapter 4 Cubes and Cube Roots Ex 4.2 15

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