Q4 of 67 Page 97

How many perfect cubes are there from 1 to 500? How many are perfect squares among these cubes?

13 = 1


23 = 8


33 = 27


43 = 64


53 = 125


63 = 216


73 = 343


83 = 512


Thus, there are 7 perfect cubes from 1 to 500 and 64 i.e., (82) is the only perfect square.


More from this chapter

All 67 →
2

Find the cubes of the first five odd natural numbers and the cubes of the first five even natural numbers. What can you say about the parity of the odd cubes and even cubes?

 3

How many perfect cubes you can find from 1 to 100? How many from –100 to 100?

 5

Find the cubes of 10, 30, 100, 1000. What can you say about the zeros at the end?

 6

What are the digits in the unit’s place of the cubes of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10? Is it possible to say that a number is not a perfect cube by looking at the digit in unit’s place of the given number, just like you did for squares?