Page 49 - Math 7

Operations on Whole Numbers

Example 7. The commander arranged his 784 soldiers in the square form for
march pass. How many soldiers were there in each row.
Solution: 2 784
Let the number of soldier in each row be x. 2 392

Then, total number of soldiers = x × x 2 196
2 98
or, x = 784
2
7 49
or, x = 2 × 2 × 7 2
2
2
2
7
or, x = (2 × 2 × 7) 2 ? 784 = 2 × 2 × 2 × 2 × 7 × 7
2
2
2
? x = 2 × 2 × 7 = 28 = 2 × 2 × 7 2
784 = 2 × 2 × 7 = 28
Hence, the number of soldiers in each row was 28.
Example 8. Find the smallest number by which when 180 is multiplied it becomes
a perfect square.
Solution:
2 180
2 90 In 180 = 2 × 3 × 5, two
2
3
3 45 numbers 2 and 3 are perfect
2
2
3 15 square but 5 is not. So, to
5 make 5 a perfect square it is
multiplied by 5.
? 180 = 2 × 2 × 3 × 3 × 5 = 2 × 3 × 5
2
2
Hence, the required smallest number is 5.
Example 9. Find the least number which is to be subtracted from 6090 to make
it a perfect square.
Solution:
7 60 90 78
+ 7 – 49 I understood!
148 1190 6090 is not a perfect square because of the
remainder 6. So, the remainder 9 should be
+ 8 –1184 subtracted to make it a perfect square.
156 6
So, the required least number to be subtracted is 6.
Example 10. Find the least number which is to be added to 3993 to make it a
perfect square.
Solution: 2
Here, 6 39 93 63 3993 is greater than 63 . So, by
adding the least number it should be
+ 6 – 36 equal to 64 = 4096.
2
123 393 Now, what should be added to 3993
+ 3 –369 to make it 4096?
126 24 It is 4096 – 3993.
Here, 64 = 4096
2
? The required least number to be added = 4096 – 3993 = 103
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 47 Vedanta Excel in Mathematics - Book 7