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CBSE NCERT Solutions for Class 8 Maths Chapter 7:
Parikshit makes a cuboid of plasticine of sides 5cm, 2cm, 5cm. How many such cuboids will he need to form a cube?
Given numbers = 5 x 2 x5
Since, Factors of 5 and 2 both are not in group of three.
Therefore, the number must be multiplied by 2 x 2 x 5 = 20 to make it a perfect cube.
Hence he needs 20cuboids.
State true or false:
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeroes.
(iii) If square of a number ends with 5, then its cube ends with25.
(iv) There is no perfect cube which ends with8.
(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.
Since, 13= 1,33= 27,53= 125, ........................ are all odd.
Since, a perfect cube ends with three zeroes.
e.g. 103= 1000,203= 8000, 303= 27000, .................. so on
Since, 52= 25, 53= 125, 152= 225, 153 = 3375
( Did not end with 25)
Since 123= 1728 [Ends with 8]
And 223= 10648 [ Ends with 8 ]
Since 103= 1000 [ Four digit number ]
And 113= 1331 [Four digit number]
Since 993= 970299 [ Six digit number ]
13= 1 [ Six digit number ]
23= 8 [ Six digit number]
You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768.
(i) We know that 103= 1000 and Possible cube of 113= 1331
Since, cube of unit’s digit 13 = 1
Therefore, cube root of 1331 is 11.
We know that 73=343
Next number comes with 7 as unit place 173 = 4913
Hence, cube root of 4913 is17.
We know that 33=27
Here in cube, ones digit is7
Now next number with 3 as ones digit 133 = 2197
And next number with 3 as ones digit 233 = 12167
Hence cube root of 12167 is23.
We know that 23=8
Here in cube, ones digit is8
Now next number with 2 as ones digit 123 = 1728
And next number with 2 as ones digit 223 = 10648
And next number with 2 as ones digit 323 = 32768
Hence cube root of 32768 is32.