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Cube and cube roots Class 8 worksheet




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Long Answer type questions

Question 1
Find the cube roots by prime factorization method
(i) 15625
(ii) 2744
(iii) 125/2197
(iv) 5832
(v) 64000
(vi) 10648
(vii) 1331
(viii) 1728

Answer

(i) 15625=5×5×5×5×5×5
315625=5
(ii) 2744=23×73
32744=2×7=14
(iii) 125/2197=(5x5x5)/(13×13×13)
3125/2197=5/13
(iv) 5832= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
35832=2×3×3=18
(v)64000 = 4 x 4 x 4 x 10 x 10 x 10
364000=4×10=40
(vi) 10648= 2 x 2 x 2 x 11 x 11 x 11
310648=2×11=22
(vii) 1331=11 x 11 x 11
31331=11
(viii) 1728= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
31728=12



Question 2
Find the cubes of these numbers.
(i) .4
(ii) 8
(iii)15
(iv).02
(v) 1.1
(vi).011

Answer

(i) .43=.046
(ii) 83=512
(iii) 153=3375
(iv) .023=.000008
(v)1.13=1.331
(vi).0113=.000001331


Question 3
Is 256 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Answer

256=28=23×23×22
Therefore it is not a perfect cube
So, it must be divided by 4 to become perfect cube


Question 4
if 6n+2=1296, then 3n+727 is

Answer

6n+2=1296
6n+2=64
n+2=4 or n=2
Now 3n+727=32+727=3729=9


Question 5
Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

Answer

Let the number be x,2x,3x
Now
x3+8x3+27x3=4500
36x3=4500 or x3=125
x=5
So numbers are 5,10,15


Question 6
If 3157464=54, then find the value
3157.464+3.157464+3.000157464

Answer

3157.464+3.157464+3.000157464=5.4+.54+.054=5.994


Fill in the blanks

Question 7
(i)The least number by which 72 be multiplied to make it a perfect cube is _____________
(ii)If 8x3=216, then x ix ____
(iii) The cube of .5 is _____
(iv) There are _________ perfect cubes between 1 and 1000.
(v) The digit at the ones place of 233 is ____
(vi) The cube of the even natural number is ____

Answer

(i)3
(ii)3
(iii).125
(iv) 8
(v)7
(vi) even


True and False

Question 8
(i)648 is not perfect cube?
(ii) 999 is a perfect cube
(iii)Square of a number is positive, so the cube of that number will also be positive
(iv) 125×8×27 is a perfect cube
(v) For an integer p, p3 is always greater than p2
(vi).83=5.12

Answer

(i)True
(ii) false
(iii) false
(iv) True
(v)False
(vi) False


Multiple Choice questions

Question 9
Cube root of the expression 1252
(a)5
(b)25
(c)10
(d)125
Question 10
which of these is a perfect cube
(a) 216
(b) 392
(b) 8640
(d) 243
Question 11
which of these is not a perfect cube
(a)729
(b)2197
(c)-1331
(d)169
Question 12
3.027 is
(a).3
(b) .03
(c).94
(d).33
Question 13
3216×27 is
(a)12
(b)18
(c)21
(d)36
Question 14
If m is the cube root of n, then n is
(a)3m
(b) 3m
(c) m/3
(d) m3
Question 15
(1310)3 is
(a) 131000
(b) 2271000
(c) 391000
(d) 21971000
Question 16
The volume of the cube is 5832m3 , the side is
(a) 18m
(b) 16 m
(c) 28 m
(d) 19m
Question 17
3827+317281331
(a) 22/33
(b) 16/11
(c) 11/16
(d) 11/3
Question 18
which of the following expression 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
Question 19
The surface area of a cube whose volume is 8m3
(a) 32m2
(b) 24m2
(c) 12m2
(d) None of these
Question 20
A cuboid of dimensions 16m, 4m, 125m has been melted to form a cube. Find the side of the cube
(a) 20m
(b) 16m
(c) 5m
(d) None of these

Answer

9. (b)
1252=125×125
So 31252=315×125=5×=25
10. (a)
11. (d)
12. (a)
13. (b)
14. (d)
15 .(d)
16. (a)
17. (b)
3827+317281331=23+1211=4833=1611
18. (d)
19. (b)
a3=8 or a=2
Surface area=6a2=24
20. (a)
a3=16×4×125
a=20



Match the Column

Question 21
Cube and cube roots class 8 worksheet

Answer

(p) -> (iii)
(q) -> (iv)
(r) -> (v)
(s) -> (ii)
(t) -> (i)


Summary

This Cube and cube roots class 8 worksheet is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feebback on the mail.

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