Question
Question Find the largest number of 5 digits, which is perfect square A. 99999 B. 99764 C. 99976 D. 99856
Ask by Mcguire Herrera. in India
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The largest 5-digit perfect square is 99856.
Solution
To determine the largest 5-digit perfect square from the given options, let's analyze each choice:
1. **Option A: 99999**
- The square root of 99999 is approximately 316.226.
- \( 316^2 = 99856 \) and \( 317^2 = 100489 \).
- 99999 is not a perfect square since it doesn't equal \( 316^2 \) or \( 317^2 \).
2. **Option B: 99764**
- The square root of 99764 is between 315 and 316.
- \( 315^2 = 99225 \) and \( 316^2 = 99856 \).
- 99764 is not a perfect square.
3. **Option C: 99976**
- The square root of 99976 is also between 316 and 317.
- \( 316^2 = 99856 \) and \( 317^2 = 100489 \).
- 99976 is not a perfect square.
4. **Option D: 99856**
- Calculating the square:
\[
316^2 = 316 \times 316 = 99856
\]
- 99856 is exactly \( 316^2 \), making it a perfect square.
**Conclusion:** The largest 5-digit perfect square among the given options is **99856**.
**Answer:** D. 99856
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Simplify this solution Bonus Knowledge
To find the largest 5-digit perfect square, we start by examining the largest 5-digit number, which is 99999. The square root of 99999 is approximately 316.22. The largest integer less than this is 316. When we square 316, we get 99856, which is indeed a perfect square. The other options are either less than this or not perfect squares. The number 99856 stands out as the highest perfect square among your options. Fun fact: perfect squares have a unique property where they look like a rectangular area through multiplication. In 2D, it's like arranging square tiles into a perfect square!
