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Answer :
To determine if 164 is a perfect square, we need to see if there is a whole number that, when multiplied by itself, would result in 164.
1. Understanding Perfect Squares:
- A perfect square is a number that can be expressed as the square of an integer.
- For example, 1, 4, 9, 16, 25, etc., are perfect squares because they are 1×1, 2×2, 3×3, 4×4, 5×5, and so on.
2. Checking 164:
- We need to find if there is any integer [tex]\( n \)[/tex] such that [tex]\( n \times n = 164 \)[/tex].
3. Square Root Estimation:
- The square root of 164 is approximately between 12 and 13 (since 12×12 = 144 and 13×13 = 169).
4. Integer Verification:
- If 12 was the exact square root, multiplying 12×12 would give 144, which is less than 164.
- If 13 was the exact square root, multiplying 13×13 would give 169, which is greater than 164.
5. Conclusion:
- Since there is no integer [tex]\( n \)[/tex] for which [tex]\( n \times n = 164 \)[/tex], 164 is not a perfect square.
Therefore, the correct answer is: "No, because there is no whole number that when multiplied by itself gives 164."
1. Understanding Perfect Squares:
- A perfect square is a number that can be expressed as the square of an integer.
- For example, 1, 4, 9, 16, 25, etc., are perfect squares because they are 1×1, 2×2, 3×3, 4×4, 5×5, and so on.
2. Checking 164:
- We need to find if there is any integer [tex]\( n \)[/tex] such that [tex]\( n \times n = 164 \)[/tex].
3. Square Root Estimation:
- The square root of 164 is approximately between 12 and 13 (since 12×12 = 144 and 13×13 = 169).
4. Integer Verification:
- If 12 was the exact square root, multiplying 12×12 would give 144, which is less than 164.
- If 13 was the exact square root, multiplying 13×13 would give 169, which is greater than 164.
5. Conclusion:
- Since there is no integer [tex]\( n \)[/tex] for which [tex]\( n \times n = 164 \)[/tex], 164 is not a perfect square.
Therefore, the correct answer is: "No, because there is no whole number that when multiplied by itself gives 164."
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