8th Maths 7.2
Chapter 7
Cubes and Cube Roots
NCERT Class 8th solution of Exercise 7.1
Exercise 7.2
Cube Roots you must learn
3√1=1
3√8=2
3√27=3
3√64=4
3√125=5
3√216=6
3√343=7
3√512=8
3√729=9
3√1000=10
3√1331=11
3√1728=12
3√2197=13
3√2744=14
3√3375=15
3√4096=16
3√4913=17
3√5832=18
3√6859=19
3√8000=20
Q1 Find the cube root of each of the following numbers by prime factorisation method.
i) 64
ii) 512
iii) 10648
iv) 27000
v) 15625
vi) 13824
vii) 110592
viii) 46656
ix) 175616
x) 91125
Sol.
i)
Prime factorisations of
3√64=2×2×2̲×2×2×2̲
=2×2
=4
Answer:
The cuberoot of 64 is 4.
ii)
Prime factorisations of
3√512=2×2×2̲×2×2×2̲×2×2×2̲
=2×2×2
=8
Answer:
The cuberoot of 512 is 8.
iii)
Prime factorisations of
3√10648=2×2×2̲×11×11×11̲
=2×11
=22
Answer:
The cuberoot of 10648 is 22.
iv)
Prime factorisations of
3√27000=2×2×2̲×3×3×3̲×5×5×5̲
=2×3×5
=30
Answer:
The cuberoot of 27000 is 30.
v)
Prime factorisations of
3√15625=5×5×5̲×5×5×5̲
=5×5
=25
Answer:
The cuberoot of 15625 is 25.
vi)
Prime factorisations of
3√13824=2×2×2̲×2×2×2̲×2×2×2̲×3×3×3̲
=2×2×2×3
=24
Answer:
The cuberoot of 13824 is 24.
vii)
Prime factorisations of
3√110952=2×2×2̲×2×2×2̲×2×2×2̲×2×2×2̲×3×3×3̲
=2×2×2×2×3
=48
Answer:
The cuberoot of 110952 is 48.
viii)
Prime factorisations of
3√46656=2×2×2̲×2×2×2̲×3×3×3̲×3×3×3̲
=2×2×3×3
=36
Answer:
The cuberoot of 46656 is 36.
ix)
Prime factorisations of
3√175616=2×2×2̲×2×2×2̲×2×2×2̲×2×2×2̲×2×2×2̲×7×7×7̲
=2×2×2×7
=56
Answer:
The cuberoot of 175616 is 56.
x)
Prime factorisations of
3√91125=3×3×3̲×5×5×5̲
=3×3×5
=45
Answer:
The cuberoot of 91125 is 45.
Q2. State true or false.
i) Cube of any odd number is even.
ii) A perfect cube does not end with two zeros.
iii) If square of a number ends with 5, then its cube ends with 25.
iv) There is no perfect cube which ends with 8.
v) The cube of a two digit number may be a three digit number.
vi) The cube of a two digit number may have seven or more digits.
vii) The cube of a single digit number may be a single digit number.
Answer:
i) False, ii)True, iii) False, iv) False,v) False, vi) False,vii) True
Q3. You are told that 1331 is a perfect cube. Can your gues without factorisation what is its cube root? Similarly, guess the cube roots of 4913,12167,32768.
Sol.
The given perfect cube 1331
Making groups of three digits starting from the right most digit of the number
1second group 331first group
second group = 1
first group = 331
ones digit in first group is 1
ones digit cuberoot may be 1
second group has 1
estimate cuberoot of 1331 is 11
Answer:
cuberoot of 1331 is 11
i)
4913
Making groups of three digits starting from the right most digit of the number
4second group 913first group
second group = 4
first group = 913
ones digit in first group is 3
ones digit cuberoot may be 7
second group has 4
13<4<23
Ten place of cuberoot of given number 1
estimate cuberoot of 4913 is 17
Answer:
cuberoot of 4913 is 17
ii)
12167
Making groups of three digits starting from the right most digit of the number
12second group 167first group
second group = 12
first group = 167
ones digit in first group is 7
ones digit cuberoot may be 3
second group has 12
23<12<33
Ten place of cuberoot of given number 2
estimate cuberoot of 12167 is 23
Answer:
cuberoot of 12167 is 23
iii)
32768
Making groups of three digits starting from the right most digit of the number
32second group 768first group
second group = 32
first group = 768
ones digit in first group is 8
ones digit cuberoot may be 2
second group has 32
33<32<43
Ten place of cuberoot of given number 3
estimate cuberoot of 32768 is 32
Answer:
cuberoot of 32768 is 32
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