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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 3√15625=5
(ii) 2744=23×73 3√2744=2×7=14
(iii) 125/2197=(5x5x5)/(13×13×13) 3√125/2197=5/13
(iv) 5832= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 3√5832=2×3×3=18
(v)64000 = 4 x 4 x 4 x 10 x 10 x 10 3√64000=4×10=40
(vi) 10648= 2 x 2 x 2 x 11 x 11 x 11 3√10648=2×11=22
(vii) 1331=11 x 11 x 11 3√1331=11
(viii) 1728= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 3√1728=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 3√n+727 is
Answer
6n+2=1296 6n+2=64 n+2=4 or n=2
Now 3√n+727=3√2+727=3√729=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 3√157464=54, then find the value 3√157.464+3√.157464+3√.000157464
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 3√216×27 is
(a)12
(b)18
(c)21
(d)36 Question 14
If m is the cube root of n, then n is
(a)3√m
(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 3√827+3√17281331
(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
(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.