Question 10 - Figure it out - Page 44, 45 - Chapter 2 Class 8 - Power Play (Ganita Prakash)

Transcript

Question 10 64 is a square number (82) and a cube number (43). Are there other numbers that are both squares and cubes? Is there a way to describe such numbers in general?For numbers 43 and 82 43 = 64 82 = 64 Here, both cube and square numbers are equal This is only true for numbers that are perfect sixth powers, like n6 = (n3)2 = (n2)3 Thus, we can say that A number that is both a perfect square and a perfect cube must be a perfect sixth power. More Examples could be: 36 = 729 Square is 729 = 272 Cube is 729 = 93