To find the least number that should be subtracted from 106131 to form a perfect square, follow these detailed, step-by-step calculations:
1. Identify the number given:
- The number in question is 106131.
2. Find the largest perfect square less than or equal to 106131.
- To do this, we need the square root of 106131 rounded down to the nearest integer.
- The square root of 106131 is approximately 325.85. Thus, rounding down, we get 325.
- Next, calculate [tex]\( 325^2 \)[/tex]:
[tex]\[
325^2 = 325 \times 325 = 105625
\][/tex]
- So, the largest perfect square less than or equal to 106131 is 105625.
3. Calculate the difference between 106131 and the largest perfect square found:
- Subtract 105625 from 106131 to find out the least number needed to be subtracted.
[tex]\[
106131 - 105625 = 506
\][/tex]
#### Conclusion:
The least number that should be subtracted from 106131 to make it a perfect square is 506.
Therefore, if you subtract 506 from 106131, you will get 105625, which is a perfect square (specifically [tex]\( 325^2 \)[/tex]).
