8th Maths 7.2
Chapter 7
Cubes and Cube Roots
NCERT Class 8th solution of Exercise 7.1
Exercise 7.2
`text {Cube Roots you must learn}`
`root [3]{1}=1`
`root [3]{8}=2`
`root [3]{27}=3`
`root [3]{64}=4`
`root [3]{125}=5`
`root [3]{216}=6`
`root [3]{343}=7`
`root [3]{512}=8`
`root [3]{729}=9`
`root [3]{1000}=10`
`root [3]{1331}=11`
`root [3]{1728}=12`
`root [3]{2197}=13`
`root [3]{2744}=14`
`root [3]{3375}=15`
`root [3]{4096}=16`
`root [3]{4913}=17`
`root [3]{5832}=18`
`root [3]{6859}=19`
`root [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`
`text{Sol.}`
i)
`text{Prime factorisations of}`
`root [3]{64} = underline(2times2times2)times underline(2times2times2)`
`=2times2`
`=4`
`text{Answer:}`
`text{The cuberoot of 64 is 4.}`
ii)
`text{Prime factorisations of}`
`root [3]{512} =underline(2times2times2)times underline(2times2times2)times underline(2times2times2)`
`=2times2times2`
`=8`
`text{Answer:}`
`text{The cuberoot of 512 is 8.}`
iii)
`text{Prime factorisations of}`
`root [3]{10648}=underline(2times2times2)times underline(11times11times11)`
`=2times11`
`=22`
`text{Answer:}`
`text{The cuberoot of 10648 is 22.}`
iv)
`text{Prime factorisations of}`
`root [3]{27000}=underline(2times2times2)times underline(3times3times3)times underline(5times5times5)`
`=2times3times5`
`=30`
`text{Answer:}`
`text{The cuberoot of 27000 is 30.}`
v)
`text{Prime factorisations of}`
`root [3]{15625}=underline(5times5times5)times underline(5times5times5)`
`=5times5`
`=25`
`text{Answer:}`
`text{The cuberoot of 15625 is 25.}`
vi)
`text{Prime factorisations of}`
`root [3]{13824}=underline(2times2times2)times underline(2times2times2)``times underline(2times2times2)times underline(3times3times3)`
`=2times2times2times3`
`=24`
`text{Answer:}`
`text{The cuberoot of 13824 is 24.}`
vii)
`text{Prime factorisations of}`
`root [3]{110952}=underline(2times2times2)``times underline(2times2times2)``times underline(2times2times2)``times underline(2times2times2)``times underline(3times3times3)`
`=2times2times2times2times3`
`=48`
`text{Answer:}`
`text{The cuberoot of 110952 is 48.}`
viii)
`text{Prime factorisations of}`
`root [3]{46656}=underline(2times2times2)times underline(2times2times2)``times underline(3times3times3)times underline(3times3times3)`
`=2times2times3times3`
`=36`
`text{Answer:}`
`text{The cuberoot of 46656 is 36.}`
ix)
`text{Prime factorisations of}`
`root [3]{175616}=underline(2times2times2)times underline(2times2times2)``times underline(2times2times2)times underline(2times2times2)``times underline(2times2times2)``times underline(7times7times7)`
`=2times2times2times7`
`=56`
`text{Answer:}`
`text{The cuberoot of 175616 is 56.}`
x)
`text{Prime factorisations of}`
`root [3]{91125}=underline(3times3times3)times underline(5times5times5)`
`=3times3times5`
`=45`
`text{Answer:}`
`text{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.
`text{Answer:}`
i) `text{False},` ii)`text{True},` iii) `text{False},` iv) `text{False},`v) `text{False},` vi) `text{False},`vii) `text{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.`
`text{Sol.}`
`text{The given perfect cube 1331}`
`text{Making groups of three digits starting from }``text{the right most digit of the number}`
`1/text{second group}text{ }331/text{first group}`
`text{second group = 1}`
`text{first group = 331}`
`text{ones digit in first group is 1}`
`text{ones digit cuberoot may be 1}`
`text{second group has 1}`
`text{estimate cuberoot of 1331 is 11}`
`text{Answer:}`
`text{cuberoot of 1331 is 11}`
i)
`4913`
`text{Making groups of three digits starting from }``text{the right most digit of the number}`
`4/text{second group}text{ }913/text{first group}`
`text{second group = 4}`
`text{first group = 913}`
`text{ones digit in first group is 3}`
`text{ones digit cuberoot may be 7}`
`text{second group has 4}`
`1^3lt4lt2^3`
`text{Ten place of cuberoot of given number 1}`
`text{estimate cuberoot of 4913 is 17}`
`text{Answer:}`
`text{cuberoot of 4913 is 17}`
ii)
`12167`
`text{Making groups of three digits starting from }``text{the right most digit of the number}`
`12/text{second group}text{ }167/text{first group}`
`text{second group = 12}`
`text{first group = 167}`
`text{ones digit in first group is 7}`
`text{ones digit cuberoot may be 3}`
`text{second group has 12}`
`2^3lt12lt3^3`
`text{Ten place of cuberoot of given number 2}`
`text{estimate cuberoot of 12167 is 23}`
`text{Answer:}`
`text{cuberoot of 12167 is 23}`
iii)
`32768`
`text{Making groups of three digits starting from }``text{the right most digit of the number}`
`32/text{second group}text{ }768/text{first group}`
`text{second group = 32}`
`text{first group = 768}`
`text{ones digit in first group is 8}`
`text{ones digit cuberoot may be 2}`
`text{second group has 32}`
`3^3 lt 32 lt 4^3`
`text{Ten place of cuberoot of given number 3}`
`text{estimate cuberoot of 32768 is 32}`
`text{Answer:}`
`text{cuberoot of 32768 is 32}`
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