Question 3 - Figure it out - Page 16, 17 - Chapter 1 Class 8 - A Square and a Cube (Ganita Prakash)

Transcript

Question 3 State true or false. Explain your reasoning. (i) Cube of any odd number is even.False 3^3 = 27 7^3 = 343 Cube of odd number is always Odd. Question 3 State true or false. Explain your reasoning. (ii) There is no perfect cube that ends with 8. False 2^3 = 8 12^3 = 1728 So, there are perfect cubes like 8 & 1728 that end with 8. Question 3 State true or false. Explain your reasoning. (iii) The cube of a 2-digit number may be a 3-digit number. False Minimum two-digit number = 10 & 10^3 = 1000 Maximum two-digit number = 99 & 99^3 = 970299 So, cube of two-digit number cannot be a 3-digit number. Question 3 State true or false. Explain your reasoning. (iv) The cube of a 2-digit number may have seven or more digits. False Minimum two-digit number = 10 & 10^3 = 1000 Maximum two-digit number = 99 & 99^3 = 970299 Since maximum two-digit number has 6 digits. Thus, cube of two-digit number cannot have seven or more digits Question 3 State true or false. Explain your reasoning. (v) Cube numbers have an odd number of factors. False Let’s consider cube number 8 Now, number 8 has factors 1, 8, 2, 4 Since it has 4 factors (even number), given statement is false