8th Maths 7.1
Chapter 7
Cubes and Cube Roots
NCERT Class 8th solution of Exercise 7.2
Exercise 7.1
Cube you must learn
13=1
23=8
33=27
43=64
53=125
63=216
73=343
83=512
93=729
103=1000
113=1331
123=1728
133=2197
143=2744
153=3375
163=4096
173=4913
183=5832
193=6859
203=8000
Q1. Which of the following numbers are not perfect cubes?
i) 216
ii) 128
iii) 1000
iv) 100
v) 46656
Sol.
i)
Prime factorisations of
216=2×2×2̲×3×3×3̲
Answer:
216 is the perfect cube.
ii)
Prime factorisations of
128=2×2×2̲×2×2×2̲×2
Answer:
128 is not perfect cube
iii)
Prime factorisations of
1000=2×2×2̲×5×5×5̲
Answer:
1000 is perfect cube
iv)
Prime factorisations of
100=2×2̲×5×5̲
Answer:
100 is not perfect cube.
v)
Prime factorisations of
46656=2×2×2̲×2×2×2̲×3×3×3̲×3×3×3̲
Answer:
46656 is perfect cube
Q2. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
i) 243
ii) 256
iii) 72
iv) 675
v) 100
i)
Prime factorisations of
243=3×3×3̲×3×3
=33×3×3
number 3 must be multiplied to obtain a perfect cube.
Answer:
3
ii)
Prime factorisations of
256=2×2×2̲×2×2×2̲×2×2
=23×23×2×2
number 2 must be multiplied to obtain a perfect cube.
Answer:
2
iii)
Prime factorisations of
72=2×2×2̲×3×3
=23×3×3
number 3 must be multiplied to obtain a perfect cube.
Answer:
3
iv)
Prime factorisations of
675=3×3×3̲×5×5
=33×5×5
number 5 must be multiplied to obtain a perfect cube.
Answer:
5
v)
Prime factorisations of
100=2×2×5×5
=22×52
number 2×5=10 must be multiplied to obtain a perfect cube.
Answer:
10
Q3. Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.
i) 81
ii) 128
iii) 135
iv) 192
v) 704
Sol.
i)
Prime factorisations of
81=3×3×3̲×3
=33×3
number 3 must be divided to obtain a perfect cube.
Answer:
3
ii)
Prime factorisations of
128=2×2×2̲×2×2×2̲×2
=23×23×2
number 2 must be divided to obtain a perfect cube.
Answer:
2
iii)
Prime factorisations of
135=3×3×3̲×5
=33×5
number 5 must be divided to obtain a perfect cube.
Answer:
5
iv)
Prime factorisations of
192=2×2×2̲×2×2×2̲×3
=23×23×3
number 3 must be divided to obtain a perfect cube.
Answer:
3
v)
Prime factorisations of
704=2×2×2̲×2×2×2̲×11
=23×23×11
number 11 must be divided toobtain a perfect cube.
Answer:
11
Q4. Parikshit makes a cuboid of plasticine of sides 5cm,2cm,5cm. How many such cuboids will he need to form a cube?
Sol.
Volume of cuboid = L×B×H
=5×2×5
=50cm3
To make perfect cube we multiply
(5×2×5)(2×2×5)
(Volume of cuboid)(2×2×5)
(Volume of cuboid)(20)
Answer:
20 cuboids will he need to form a cube.
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