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Find the least number which must be added to each of the following numbers in order to get a
perfect square. Also, find the square root of the perfect square so obtained.
(i) 437
(v) 6352
(ii) 731
(vi) 9317
(iii) 936
(iv) 2478

Sagot :

GinnyAnsweridn
To find the least number that must be added to a given number to get a perfect square, and to determine the square root of that perfect square, we can follow these steps. Here's the detailed solution for each number:

1. Number: 437
- The least number to add to 437 to get a perfect square is 4.
- The perfect square obtained is 441 (437 + 4).
- The square root of 441 is 21.

So, the least number to add is [tex]\( 4 \)[/tex] and the square root is [tex]\( 21 \)[/tex].

2. Number: 6352
- The least number to add to 6352 to get a perfect square is 48.
- The perfect square obtained is 6400 (6352 + 48).
- The square root of 6400 is 80.

So, the least number to add is [tex]\( 48 \)[/tex] and the square root is [tex]\( 80 \)[/tex].

3. Number: 731
- The least number to add to 731 to get a perfect square is 53.
- The perfect square obtained is 784 (731 + 53).
- The square root of 784 is 28.

So, the least number to add is [tex]\( 53 \)[/tex] and the square root is [tex]\( 28 \)[/tex].

4. Number: 2478
- The least number to add to 2478 to get a perfect square is 22.
- The perfect square obtained is 2500 (2478 + 22).
- The square root of 2500 is 50.

So, the least number to add is [tex]\( 22 \)[/tex] and the square root is [tex]\( 50 \)[/tex].

5. Number: 936
- The least number to add to 936 to get a perfect square is 25.
- The perfect square obtained is 961 (936 + 25).
- The square root of 961 is 31.

So, the least number to add is [tex]\( 25 \)[/tex] and the square root is [tex]\( 31 \)[/tex].

6. Number: 9317
- The least number to add to 9317 to get a perfect square is 92.
- The perfect square obtained is 9409 (9317 + 92).
- The square root of 9409 is 97.

So, the least number to add is [tex]\( 92 \)[/tex] and the square root is [tex]\( 97 \)[/tex].

Summarizing:
- For [tex]\( 437 \)[/tex]: Add [tex]\( 4 \)[/tex] to get a perfect square with a square root of [tex]\( 21 \)[/tex].
- For [tex]\( 731 \)[/tex]: Add [tex]\( 53 \)[/tex] to get a perfect square with a square root of [tex]\( 28 \)[/tex].
- For [tex]\( 936 \)[/tex]: Add [tex]\( 25 \)[/tex] to get a perfect square with a square root of [tex]\( 31 \)[/tex].
- For [tex]\( 2478 \)[/tex]: Add [tex]\( 22 \)[/tex] to get a perfect square with a square root of [tex]\( 50 \)[/tex].
- For [tex]\( 6352 \)[/tex]: Add [tex]\( 48 \)[/tex] to get a perfect square with a square root of [tex]\( 80 \)[/tex].
- For [tex]\( 9317 \)[/tex]: Add [tex]\( 92 \)[/tex] to get a perfect square with a square root of [tex]\( 97 \)[/tex].
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