Class 8 Maths - Cubes and Cubes Roots CBSE Worksheets Solutions

Multiple Choice Questions

The number 125  can be expressed as a power of five: 5 ³

Substitute the base into the expression to get which simplifies to using the exponent rule
The cube root operation is the same as raising to the power of 1/3 . The expression becomes . Applying the exponent rule again gives

Q2: Which of these is a perfect cube
(a) 216
(b) 392
(c) 8640
(d) 243
Ans: (a)

Q3: Which of these is not a perfect cube
(a) 729
(b) 2197
(c) -1331
(d) 169
Ans: (d)

169= 13×13

Q4: ₃√.027 is
(a) .3
(b) .03
(c) .94
(d) .33
Ans: (a)

Q5: ₃√216×-27 is
(a)12
(b)-18
(c)21
(d)36
Ans: (b)

Q6: If m is the cube root of n, then n is
(a)₃√m
(b) 3m
(c) m/3
(d) m³

^{Ans: (d)}

Q7: The one’s digit of the cube of 53 is:

(a) 9

(b) 3

(c) 7

(d)  1

Ans: (c)

Q8: The volume of the cube is 5832m³ , the side is
(a) 18m
(b) 16 m
(c) 28 m
(d) 19m

^{Ans: (a)}

Q9:
(a) 22/33
(b) 58/33
(c) 11/16
(d) 11/3

^{Ans: (b)}

Q10: Which of the following expressions is not a perfect cube
(a) 27 x 125 x 64
(b) 1331 x 125 x 8
(c) 15 x 8 x 25 x 9
(d) None of these
Ans: (d)

A perfect cube is a number that can be expressed as the cube of an integer. Since all integers in options a, b,and  c can be expressed as a cube of integers. Therefore,  None of these is the answer.

Q11: The surface area of a cube whose volume is 8m³
(a) 32m²
(b) 24m²
(c) 12m²
(d) None of these
^Ans: (b)

a³=8 

=> a=2
Surface area=6a²=24

Q12: A cuboid of dimensions 16m, 4m, 125m has been melted to form a cube. Find the side of the cube
(a) 20m
(b) 1616m
(c) 55m
(d) None of these

Ans: (a)
lbh=16×4×125 = 8000
a³=8000

=>a=20m

True and False

Q2: 999 is a perfect cube.
Ans: False

Q3: The square of a number is positive, so the cube of that number will also be positive.
Ans: False

Q4: 125×8×27 is a perfect cube.
Ans: True

Q5: For an integer p, p³ is always greater than p²​_.​​​​​​
Ans: False

Q6: 8³ = 5.12
Ans: False

Fill in the blanks

Q1: The least number by which 72 be multiplied to make it a perfect cube is __________.
Ans: 3

Q2: If 8x³=216, then x is ____
Ans: 3

Q3: The cube of .5 is _____
Ans: .125

Q4: There are _________ perfect cubes between 1 and 1000.
Ans: 8

Q5: The digit at the ones place of 23³ is ____
Ans: 7

Q6: The cube of the even natural number is ____
Ans: even

Find the cube roots by prime factorization method

Q1: 15625
Ans: 15625=5×5×5×5×5×5

₃√15625=25

Q2: 2744
Ans: 2744=2³×7³
₃√2744=2×7=14

Q3: 125/2197
Ans: 125/2197=(5x5x5)/(13×13×13)
₃√125/2197=5/13

Q4: 5832
Ans: 5832= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
₃√5832=2×3×3=18

Q5: 64000
Ans: 64000 = 4 x 4 x 4 x 10 x 10 x 10
₃√64000=4×10=40

Answer the following questions

Q1: Is 256 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Ans: 256=2⁸=2³×2³×2²
Therefore, it is not a perfect cube
So, it must be divided by 4 to become a perfect cube

Q2: if 6ⁿ⁺²=12966, then ₃√n+727 is
Ans: 6ⁿ⁺²=1296
6ⁿ⁺²=6⁴
n+2=4 or n=2
Now ₃√n+727=₃√2+727=₃√729=9

Q3: Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
Ans: Let the number be x,2x,3x
Now
x³+8x³+27x³=4500
36x³=4500

x³=4500/36
x³=125
x=5
So the numbers are 5,10,15

Q4: If ₃√157464=54, then find the value
₃√157.464+₃√.157464+₃√.000157464
Ans: 
₃√157.464+₃√.157464+₃√.000157464 = 5.4+.54+.054 

5.4+.54+.054 = 5.994