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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 \times 5 \times 5 \times 5 \times 5 \times 5 $
$\sqrt[3]{15625} =5$
(ii) $2744= 2^3 \times 7^3$
$\sqrt[3]{2744} =2 \times 7=14$
(iii) $125/2197= (5 x 5 x 5) / (13 \times 13 \times 13)$
$\sqrt[3]{125/2197} =5 /13$
(iv) 5832= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3
$\sqrt[3]{5832} =2 \times 3 \times 3=18$
(v)64000 = 4 x 4 x 4 x 10 x 10 x 10
$\sqrt[3]{64000} =4 \times 10 =40$
(vi) 10648= 2 x 2 x 2 x 11 x 11 x 11
$\sqrt[3]{10648} =2 \times 11 =22$
(vii) 1331=11 x 11 x 11
$\sqrt[3]{1331} =11$
(viii) 1728= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3
$\sqrt[3]{1728} =12$

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

Answer

(i) $.4^3 = .046 $
(ii) $8^3= 512$
(iii) $15^3=3375$
(iv) $.02^3= .000008$
(v)$1.1^3= 1.331$
(vi)$.011^3= .000001331$

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

$256= 2^8= 2^3 \times 2^3 \times 2^2$
Therefore it is not a perfect cube
So, it must be divided by 4 to become perfect cube

Question 4
if $6^{n+2}=1296$, then $\sqrt[3]{n + 727}$ is

Answer

$6^{n+2}=1296$
$6^{n+2}=6^4$
$n+2=4$ or $n=2$
Now $\sqrt[3]{n + 727}= \sqrt[3]{2 + 727}=\sqrt[3]{729}=9$

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
$x^3 + 8x^3 + 27x^3=4500$
$36x^3=4500$ or $x^3=125$
$x=5$
So numbers are 5,10,15

Question 6
If $\sqrt[3]{157464}=54$, then find the value
$\sqrt[3]{157.464}+ \sqrt[3]{.157464}+ \sqrt[3]{.000157464}$

Answer

$\sqrt[3]{157.464}+ \sqrt[3]{.157464}+ \sqrt[3]{.000157464}=5.4 + .54 + .054=5.994$

Fill in the blanks

Question 7
(i)The least number by which 72 be multiplied to make it a perfect cube is _____________
(ii)If $8x^3=216$, 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 $23^3$ 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) $125 \times 8 \times 27$ is a perfect cube
(v) For an integer p, $p^3$ is always greater than $p^2$
(vi)$.8^3=5.12$

Answer

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

Multiple Choice questions

Question 9
Cube root of the expression $125^2$
(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
$\sqrt [3]{.027} $ is
(a).3
(b) .03
(c).94
(d).33
Question 13
$\sqrt [3]{216 \times 27} $ is
(a)12
(b)18
(c)21
(d)36
Question 14
If m is the cube root of n, then n is
(a)$\sqrt [3]{m} $
(b) 3m
(c) m/3
(d) $m^3$
Question 15
$(1 \frac {3}{10})^3$ is
(a) $1 \frac {3}{1000}$
(b) $2 \frac {27}{1000}$
(c) $3 \frac {9}{1000}$
(d) $2 \frac {197}{1000}$
Question 16
The volume of the cube is $5832m^3$ , the side is
(a) 18m
(b) 16 m
(c) 28 m
(d) 19m
Question 17
$\sqrt [3]{\frac {8}{27}} + \sqrt [3]{\frac {1728}{1331}} $
(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 $8m^3$
(a) $32m^2$
(b) $24m^2$
(c) $12m^2$
(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) $20$m
(b) $16$m
(c) $5$m
(d) None of these

Answer

9. (b)
$125^2= 125 \times 125$
So $\sqrt[3]{125^2}=\sqrt[3]{15 \times 125}=5 \times =25$
10. (a)
11. (d)
12. (a)
13. (b)
14. (d)
15 .(d)
16. (a)
17. (b)
$\sqrt [3]{\frac {8}{27}} + \sqrt [3]{\frac {1728}{1331}} = \frac {2}{3} + \frac {12}{11} = \frac {48}{33} = \frac {16}{11}$
18. (d)
19. (b)
$a^3=8$ or $a=2$
Surface area=$6a^2=24$
20. (a)
$a^3=16 \times 4 \times 125$
$a=20$

Match the Column

Question 21

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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