8th Maths 7.1
Chapter 7
Cubes and Cube Roots
NCERT Class 8th solution of Exercise 7.2
Exercise 7.1
`text {Cube you must learn}`
`1^3=1`
`2^3=8`
`3^3=27`
`4^3=64`
`5^3=125`
`6^3=216`
`7^3=343`
`8^3=512`
`9^3=729`
`10^3=1000`
`11^3=1331`
`12^3=1728`
`13^3=2197`
`14^3=2744`
`15^3=3375`
`16^3=4096`
`17^3=4913`
`18^3=5832`
`19^3=6859`
`20^3=8000`
Q1. Which of the following numbers are not perfect cubes?
i) `216`
ii) `128`
iii) `1000`
iv) `100`
v) `46656`
`text{Sol.}`
i)
`text{Prime factorisations of}`
`216=underline(2times2times2)times underline(3times3times3)`
`text{Answer:}`
`text{216 is the perfect cube.}`
ii)
`text{Prime factorisations of}`
`128=underline(2times2times2)times underline(2times2times2)times2`
`text{Answer:}`
`text{128 is not perfect cube}`
iii)
`text{Prime factorisations of}`
`1000=underline(2times2times2)times underline(5times5times5)`
`text{Answer:}`
`text{1000 is perfect cube}`
iv)
`text{Prime factorisations of}`
`100=underline(2times2)timesunderline(5times5)`
`text{Answer:}`
`text{100 is not perfect cube.}`
v)
`text{Prime factorisations of}`
`46656=underline(2times2times2)timesunderline(2times2times2)``timesunderline(3times3times3)``times underline(3times3times3)`
`text{Answer:}`
`text{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)
`text{Prime factorisations of}`
`243=underline(3times3times3)times3times3`
`=3^3times3times3`
`text{number 3 must be multiplied to}``text{ obtain a perfect cube.}`
`text{Answer:}`
`3`
ii)
`text{Prime factorisations of}`
`256=underline(2times2times2)times underline(2times2times2)times2times2`
`=2^3times2^3times2times2`
`text{number 2 must be multiplied to}``text{ obtain a perfect cube.}`
`text{Answer:}`
`2`
iii)
`text{Prime factorisations of}`
`72=underline(2times2times2)times3times3`
`=2^3times3times3`
`text{number 3 must be multiplied to}``text{ obtain a perfect cube.}`
`text{Answer:}`
`3`
iv)
`text{Prime factorisations of}`
`675=underline(3times3times3)times5times5`
`=3^3times5times5`
`text{number 5 must be multiplied to}``text{ obtain a perfect cube.}`
`text{Answer:}`
`5`
v)
`text{Prime factorisations of}`
`100=2times2times5times5`
`=2^2times5^2`
`text{number } 2times5=10text{ must be multiplied to}``text{ obtain a perfect cube.}`
`text{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`
`text{Sol.}`
i)
`text{Prime factorisations of}`
`81=underline(3times3times3)times3`
`=3^3times3`
`text{number 3 must be divided to``text{ obtain a perfect cube.}`
`text{Answer:}`
`3`
ii)
`text{Prime factorisations of}`
`128=underline(2times2times2)times underline(2times2times2)times2`
`=2^3times2^3times2`
`text{number 2 must be divided to``text{ obtain a perfect cube.}`
`text{Answer:}`
`2`
iii)
`text{Prime factorisations of}`
`135=underline(3times3times3)times5`
`=3^3times5`
`text{number 5 must be divided to``text{ obtain a perfect cube.}`
`text{Answer:}`
`5`
iv)
`text{Prime factorisations of}`
`192=underline(2times2times2)times underline(2times2times2)times3`
`=2^3times2^3times3`
`text{number 3 must be divided to``text{ obtain a perfect cube.}`
`text{Answer:}`
`3`
v)
`text{Prime factorisations of}`
`704=underline(2times2times2)times underline(2times2times2)times11`
`=2^3times2^3times11`
`text{number 11 must be divided to``text{obtain a perfect cube.}`
`text{Answer:}`
`11`
Q4. Parikshit makes a cuboid of plasticine of sides `5text{cm}, 2 text{cm}, 5text{cm}.` How many such cuboids will he need to form a cube?
`text{Sol.}`
`text{Volume of cuboid = L}timestext{B}timestext{H}`
`=5times2times5`
`=50text{cm}^3`
`text{To make perfect cube we multiply}`
`(5times2times5)(2times2times5)`
`(text{Volume of cuboid})(2times2times5)`
`(text{Volume of cuboid})(20)`
`text{Answer:}`
`text{20 cuboids will he need to form a cube.}`
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