Answered

Connect with knowledgeable individuals and get your questions answered on IDNLearn.com. Ask your questions and get detailed, reliable answers from our community of experienced experts.

Find the least number that should be subtracted from the following number to set a perfect square:

[tex]\[ 106131 \][/tex]

[tex]\[ 1 \leq 770 \][/tex]

Sagot :

GinnyAnsweridn
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]).
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.