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 to obtain 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. **Make pairs from the right**: 4 | 02
2. **Find the largest perfect square less than or equal to 4**: The perfect square is 4 (which is \(2^2\)).
3. **Subtract**: \(4 - 4 = 0\). Bring down the next pair (02) to get 02.
4. **Double the root found (2)**: \(2 \times 2 = 4\).
5. **Find a digit (x) such that \(4x \times x < 2\)**: The only digit that works is 0, since \(40 \times 0 = 0 < 2\).
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