Page 65 - Start Up Mathematics_8 (Non CCE)

Step 4: Subtract the product (square) from the first period (57 – 49 = 8).
Step 5: Bring down the second period (15) and place it to the right of the remainder. This number (815)
forms the new dividend.
Step 6: (i) Double the quotient (7 × 2 = 14) and write it in the divisor’s place followed by a blank space.
(ii) Fill the blank space with the largest number (5) such that 145 × 5 is less than 815. 145 is the
new divisor.
Step 7: Subtract the product (145 × 5 = 725) from the dividend obtained in step 5. Bring down the third
period (36) to the right of the remainder. This again forms the new dividend, i.e., 9,036.
Step 8: Repeat steps 6, 7 till all the periods are exhausted.
Step 9: The final quotient (756) is the square root of 5,71,536.

The number of bars is equal to the number of digits in the square root of the given number.

Example 17: Find the least number that must be subtracted from 4,568 to make it 67
a perfect square. Also, find the square root of the resulting number. 6 45 68
Solution: The remainder is 79. It means that if 79 is subtracted from the 36
given number, the remainder will be zero, and, the given number
will become a perfect square. 127 968
Thus, the least number to be subtracted is 79. 889
\ Perfect square = 4,568 – 79 = 4,489 79
4,489 = 67

Example 18: Find the least number that must be added
to 8,902 to make it a perfect square. Find
the square root of the perfect square so 94 95
obtained. 9 89 02 9 89 02

2
Solution: It is clear that (94) < 8,902 < (95) 2 81 81
2
\ 8,902 = (925 – 802) less than (95) 184 802 185 802
= 123 less than (95) 2
Thus, the least number to be added is 736 925
123.
\ Perfect square = 8,902 + 123 = 9,025

9,025 = 95

Example 19: Find the least number of six digits that is a perfect square.
Solution: Least six digit number = 1,00,000
To find the least six digit number which is a perfect square, we need to find the least number
that must be added to 1,00,000 to make it a perfect square.

316 317
3 10 00 00 3 10 00 00

9 9
61 100 61 100
61 61
626 3900 627 3900
3756 4389

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