Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.(i) 402   (ii)1989  (iii)3250  (iv) 825(v) 4000

Explanation

To find the least number that must be subtracted from each of the given numbers so that the result is a perfect square, we will use the long division method for finding square roots. Let's solve each part step by step.

### (i) For 402:
1. **Pair the digits**: Start from the right, pair the digits: (4)(02).
2. **Find the largest square**: The largest square less than or equal to 4 is 2² = 4.
3. **Subtract**: 4 - 4 = 0. Bring down the next pair (02) to get 02.
4. **Double the root**: Double the root (2) to get 4. We need to find a digit (x) such that (40 + x)x ≤ 2.
5. **Trial and error**: Trying x = 0 gives us 0, which is less than 2. Trying x = 1 gives us 41, which is greater than 2. So, we take x = 0.
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