Page 18 - 新思维数学活动用书7 样章

1.6 Square roots and cube roots

14 289 and 324 are two consecutive square numbers. Find the next square number after 324.
15 1331 and 1728 are two consecutive cube numbers. Find the next cube number after 1728.
16 a Show that 64 is a square number and a cube number.
b There is one number between 100 and 1000 that is a square number and a cube number.
What is this number?

c What method did you use to answer part b? Could you use the same method to look for
another number that is both a square number and a cube number?

17