* When a number is multiplied 3 times, it is called cube.
* Cube of a number ending with the digits 0, 1, 4, 5, 6 and 9 ends 0, 1, 4, 5, 6, and 9.
* Cube of even number is even and cube of odd number is odd.
* A perfect cube can be written as the product of triplets of prime factorization.
EXERCISE - A
a) 121
b) 1728
c) 2744
d) 256
e) 3375
f) 4000
g) 512
h) 100
2) Find the smallest number by each should be multiplied to obtain a perfect cube.
a) 121
b) 625
c) 72
d) 675
e) 100
f) 500
g) 2662
3) Find the smallest number by each should be divided to obtain a perfect cube :
a) 81
b) 135
c) 625
d) 3456
e) 192
f) 500
g) 2662
4) Find the cube of the following :
a) 6
b) 12
c) 21
d) 99
e) 302
f) 15
g) 11
h) 25
5) Write cubes of 5 natural numbers which are of the form of (3n + 1) and verify the following statement that the cube of a natural number of the form (3n + 1) is a natural number of the same form.
6) If one side of a cube is 9 metres then find its volume.
7) Rajat makes a cuboid of sides 5 cm, 4 cm and 5 cm. How many such cuboid will he need to form a cube?
8) Namita has a cuboid of sides 2 cm x 1 cm x 1 cm. How many such cuboids will she need to form a cube ?
9) Write cubes of 5 natural numbers which are the form of n² + 1 and verify the following statement that the cube of natural number of the form n²+1 is a natural number of the same form .
10) Find the cube of each of the following using (a+ b)³
a) 12
b) 17
c) 69
d)109
e) 125
e) 14
f) 102
g) 55
11) Find the cube of each of the following using (a - b)³
a) 69
b) 95
c) 999
d) 88
e) 77
f) 18
g) 99
h) 48
EXERCISE-B
1) Find the cube root of the following by Prime Factorization Method.
a) 64
b) 125
c) 512
d) 343
e) 1331
f)1728
g) 2744
h) 15625
i) 27000
j) 46656
k) 91125
l) 592704
m) 13824
2) Estimate the cube root of the following
a) 46656
b) 54872
c) 103823
d) 157464
e) 175616
f) 262144
g) 389017
h) 551368
i) 804357
j) 884736
k) 592704
l) 389017
m) 117649
n) 238328
3) The volume of a cube is 262144 cm³, find its side.
4) The volume of a cuboidal box is 74088 cm³, find its side.
5) Find the cube root of the given negative integers.
a) -64
b) -2197
c) -5832
d) -17576
EXERCISE - C
1)State true or false
a) There is no perfect cube which ends with 8.
b) The cube of a two digit number maybe a 3 digit number.
c) The cube of a single digit number maybe a single digit.
d) 1729 is a perfect cube.
e) No perfect cube can end with exactly two zeros .
f) if a divides b then a³ divides b³.
2) Choose the Correct Option
1) Find the cube of (-3/4).
a) 9/16 b) (-27/64) c) (-9/16) d) (27/16)
2) Cube of negative numbers are always _____
a) positive b) negative c) even d) odd
3) Solve : ³√343 - ³√-216.
a) 15 b) 17 c) 13 d) 12
4) Find the value of ³√(125 x 343 x 64).
a) 140 b) 135 c) 150 d) 145
5) Three cubes of edges 3cm, 4cm, and 5cm are melted to form a new cube. What is the edge of new cube?
a) 5cm b) 6cm c) 8cm d) 4cm
6) How many hundreds are in there in 31 x 2² x 5³ ?
a) 150 b) 125 c) 155 d) 120
7) How many thousands will be there in 29 x 2³ x 5³ ?
a) 29 b) 30 c) 27 d) 23
8) Simplify : (³√2197 x ³√1728)/³√1331
a) 152/10 b) 150/12 c) 155/11 d) 156/11
Miscellaneous Exercise
1) Find the cube of (3/5)³ - (1/5)³.
2) If a number is written as 3 x 3x 3x 3x 5x 3 x 7x 7 x 5x 7, then find the smallest number by which this is to be multiplied to form a perfect cube.
3) If ³√x =12. Find x.
4) A cubical box has a volume of 1331 cm³, find its surface area.
5) By which least number 125 x 512 x 4 be divided to make it a perfect cube ?
6) Find the value of ³√1.728 x ³√1.331.
7) Simplifly if 3ˣ = 243, find x.
8) Three solid wooden cubes of different colours with edges 30cm each are placed one along another. How much cubic cm of wood is required to make it ?
9) Find the volume of cube having side 7cm.
10) Find ³√-2.197.
11) Find the cube of 75 using (a+ b)³ and check your result using (a - b)³.
12) Find the cube root of 0.001728.
13) Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.
14) The volume of a cube is 343 cm³, find its side.
15) Three numbers are in the ratio 2:3:4 and sum of their cube is 33957, find the numbers.
16) Estimate the cube root of 456533.
17) Simplify {³√64 x ³√512}/{³√216 x ³√27}
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