Page 59 - ICSE Math 8

Grouping them into groups of three, we get
2 1,17,912
1,17,912 = 2 × 2 × 2 × 3 × 17 × 17 × 17 2 58,956
You can see that there is only one number 3 which is left ungrouped. 2 29,478
So if we divide 1,17,912 by 3, it becomes a perfect cube. 3 14,739
\ 1,17,912 ÷ 3 = 39,304
17 4,913
39,304 = 2 × 2 × 2 × 17 × 17 × 17 17 289

3 39 304, = 22 2171717×× × × × 17 17
3
1
2 17
\ 39 304, = 2 × 17 = 34
3
Cube root of a number by using its units digit
This method utilizes the fact that the units digit of the cube of a natural number depends upon the units digit
of the given number. Observe the following table:

Units digit of a number (n) 0 1 2 3 4 5 6 7 8 9

Units digit of the cube root of the number ( n ) 0 1 8 7 4 5 6 3 2 9
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This method is applicable for numbers upto 6 digits which are perfect cubes. It is also called the method
of estimation.

Step 1: Consider the units digit of the perfect cube whose cube root is to be calculated and determine the
units digit in the cube root from the above table.
Step 2: Strike out from the right, the last three digits of the number. If nothing is left, the digit obtained in
step 1 is the answer.
Step 3: Otherwise, determine the largest 1-digit number whose cube is less than or equal to this leftover
number. This is the tens digit of the cube root.

Example 7: Find the cube roots by using their units digit: (a) 125 (b) 91,125
Solution: (a) The units digit of 125 is 5.
fi The digit at the units place of the cube root = 5
As there is no number left after striking out the units, tens and hundreds digits of 125, so
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the required cube root is 5, i.e., 125 = 5.
(b) Units digit of the number = 5
fi Units digit of the cube root of the number = 5
The number left after striking out the units, tens and hundreds digits of 91,125 is 91.
3
 4 < 91 < 5 3
fi The tens digit of the cube root of the number = 4

\ 91125, = 45
3

EXERCISE 4.2

1. Find the smallest numbers by which the following numbers must be multiplied to make them perfect cubes.
(a) 36,000 (b) 3,456 (c) 4,116 (d) 10,976 (e) 8,232
2. Find the smallest numbers by which the following numbers must be divided to make them perfect cubes.
(a) 8,640 (b) 2,662 (c) 27,648 (d) 77,760 (e) 69,120

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