State true or false. Explain your reasoning. The cube of any odd number is even. Class 8
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State true or false. Explain your reasoning. The cube of any odd number is even. Class 8
Question 1.
State true or false. Explain your reasoning. Class 8
(i) The cube of any odd number is even.
(ii) There is no perfect cube that ends with 8.
(iii) The cube of a 2-digit number may be a 3-digit number.
(iv) The cube of a 2-digit number may have seven or more digits.
(v) Cube numbers have an odd number of factors.
Solution:
(i) False. As product of three odd numbers is odd.
(ii) False. Examples : 8 = 23, 1728 = 123, etc.
(iii) False, because cube of smallest two digit number 10 is 1000, which is a 4-digit number.
(iv) False, because cube of smallest three digit number 100 is 1000000, which is a seven digit number.
(v) False, for example :
1000 = 2 × 2 × 2 × 5 × 5 × 5 = 6 factors.