Q2. Find the least number which must be subtracted from 6203 to obtain a perfect square. Also, find the square root of the number so obtained.
Sol. The given number is 6203. ∴ 119 must be subtracted from 6203 to obtain a perfect square.
Hence the perfect square number is 6203 – 119 = 6084 and √6084 = 78.
Q3. Find the greatest number of six digits which is a prefect square. Find the square root of this number.
Sol. The greatest 6-digit number is 999999.
So, the greatest 6-digit square number is = 999999 – 1998 = 998001
and √998001 = 999
Q4. Find the least number which must be added to 6203 to obtain a prefect square. Also, find the square root of the number so obtained.
Sol. The given number is 6203.
So, 61 is the least number which when added to the given number
6023, it becomes a perfect square.
∴ Perfect square number is 6023 + 61 = 6084
and √6084 = 78.
Q5. Find the least number of six digits which is a perfect square.
Find the square root of this number.
Sol. Let the least six-digit number be 100000.
But remainder (+) ive
So we will try again to get a negative remainder
Hence 489 must be added to the given number to obtain the least perfect square of six-digit.
∴ The required number = 100000 + 489 = 100489
and √100489 = 317.