Question

(11
Find the least number which must be subtracted from 170597 to get a perfect square.
Find the least number which must be subtracted from 9545 to get a perfect square.
(i) What is the least number which must be subtracted from 123401 so that the remainder is a perfect square
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Answer 1

Step-by-step explanation:

4230 is between 60^2 & 70^2. Let us converge the search. 62^2=3844, 69^2= 62^2<4230<69^2. Again 63^2=3969.63^2-62^2=125.64^2-63^2=127. 64^2=63^2+127=3969+127=4096. Similarly 65^2-64^2=129. So 65^2=64^2+129=4096+129=4225. 4225 is the nearest square number to 4230. 4225=4230-5.

Number 5 has to subtract from 4230 to get a perfect number