Worksheet Solutions: Cube - 2 | Mental Mathematics for Class 8 PDF Download

Q1: Find the cube roots by prime factorization method
(i) 15625
(ii) 2744
(iii) 125/2197
(iv) 5832
(v) 64000
(vi) 10648
(vii) 1331
(viii) 1728
Ans:


Q2: Is 256 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
Ans: 256 = 2⁸ = 2³ × 2³ × 2² 
Therefore it is not a perfect cube
So, it must be divided by 4 to become perfect cube

Q3: Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.
Ans: Let the number be x,2x,3x
Now x³ + 8x³ + 27x³ = 4500
36x³ = 4500 or x³ = 125
x = 5
So numbers are 5,10,15

Q4: Find the cubes of these numbers.
(i) .4
(ii) 8
(iii) 15
(iv) .02
(v) 1.1
(vi) .011
Ans:
(i) .4³ = .046
(ii) 8³ = 512
(iii)15³ = 3375
(iv) .02³ = .000008
(v) 1.1³ = 1.331
(vi) .011³ = .000001331

Q5: if 6ⁿ⁺² = 1296 , then
Ans: 6ⁿ⁺² = 1296
6ⁿ⁺² = 6⁴
n + 2 = 4 or n = 2


Q6: (i)The least number by which 72 be multiplied to make it a perfect cube is _____________
(ii) If 8x³ = 216, then x ix ____
(iii) The cube of .5 is _____
(iv) There are _________ perfect cubes between 1 and 1000.
(v) The digit at the ones place of 23³ is ____
(vi) The cube of the even natural number is ____
Ans:
(i) 3
(ii) 3
(iii) .125
(iv) 8
(v) 7
(vi) even

Q7: (i) 648 is not perfect cube?
(ii) 999 is a perfect cube
(iii) Square of a number is positive, so the cube of that number will also be positive
(iv) 125 × 8 × 27 is a perfect cube
(v) For an integer p, p³ is always greater than p²
(vi) .8³ = 5.12
Ans: (i)True
(ii) false
(iii) false
(iv) True
(v)False
(vi) False

Q8: Cube root of the expression 125²
(a) 5
(b) 25
(c) 10
(d) 125
Ans: (b)


Q9: Which of these is a perfect cube
(a) 216
(b) 392
(b) 8640
(d) 243
Ans: (a)

Q10: Which of these is not a perfect cube
(a) 729
(b) 2197
(c) -1331
(d) 169
Ans: (d)