Page 64 - ICSE Math 8

THINK SMART

1. A godown is cubical in shape with each of its inner sides measuring 20 m. How many cubical boxes,
each of side length 2 m can be fitted inside the godown?
2. Misha wrote a 3-digit number such that its last two digits form the cube of 4 and the left most digit is
the cube root of a number which is 2 less than the sum of the last two digits. What number does Misha
wrote?
Maths Lab Activity

Aim: To find patterns in cubes of numbers
Procedure:
Step 1: Choose any number between 1 and 100, say 52.
3
Step 2: Find its cube, i.e., (52) = 1,40,608.
Step 3: Ignore all the digits except the last two digits of the result obtained in step 2, i.e., 08.
Step 4: Now keep repeating steps 2 and 3 as shown:
3
(08) = 512
3
(12) = 1,728
3
(28) = 21,952
3
(52) = 1,40,608
What do you observe?
You can see that after a few repetitions of steps 2 and 3, we again get the original number.
Now repeat this activity for some other numbers.

52