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A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out?
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A general wishes to draw up his 7500soliders in the form of big square...
Understanding the Problem
To determine how many soldiers are left out when arranging 7500 soldiers in a big square, we first need to find the largest perfect square that can be formed with these soldiers. A perfect square means that the number of soldiers can be arranged in an equal number of rows and columns.
Finding the Largest Square
1. **Calculate the Square Root**:
We need to find the largest integer \( n \) such that \( n^2 \) is less than or equal to 7500.
\[
n = \text{floor}(\sqrt{7500}) \approx 86.6
\]
Thus, the largest whole number is \( n = 86 \).
2. **Calculate the Perfect Square**:
Now, we calculate \( n^2 \):
\[
86^2 = 7396
\]
This means 7396 soldiers can be arranged in a square formation.
Finding Soldiers Left Out
3. **Calculate Remaining Soldiers**:
To find out how many soldiers are left out, we subtract the number of soldiers in the square from the total:
\[
\text{Left Out} = \text{Total Soldiers} - n^2 = 7500 - 7396 = 104
\]
Conclusion
- The general can arrange **7396 soldiers** in a big square.
- Therefore, there are **104 soldiers left out** after the arrangement.
This calculation helps in better organizing the soldiers during deployment.
To determine how many soldiers are left out when arranging 7500 soldiers in a big square, we first need to find the largest perfect square that can be formed with these soldiers. A perfect square means that the number of soldiers can be arranged in an equal number of rows and columns.
Finding the Largest Square
1. **Calculate the Square Root**:
We need to find the largest integer \( n \) such that \( n^2 \) is less than or equal to 7500.
\[
n = \text{floor}(\sqrt{7500}) \approx 86.6
\]
Thus, the largest whole number is \( n = 86 \).
2. **Calculate the Perfect Square**:
Now, we calculate \( n^2 \):
\[
86^2 = 7396
\]
This means 7396 soldiers can be arranged in a square formation.
Finding Soldiers Left Out
3. **Calculate Remaining Soldiers**:
To find out how many soldiers are left out, we subtract the number of soldiers in the square from the total:
\[
\text{Left Out} = \text{Total Soldiers} - n^2 = 7500 - 7396 = 104
\]
Conclusion
- The general can arrange **7396 soldiers** in a big square.
- Therefore, there are **104 soldiers left out** after the arrangement.
This calculation helps in better organizing the soldiers during deployment.
Community Answer
A general wishes to draw up his 7500soliders in the form of big square...
150 soldiers
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A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out?
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A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out?.
A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A general wishes to draw up his 7500soliders in the form of big square . After arranging he found out some of them r left out . How many soldiers r left out?.
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