which of the following is not a square 1^6. 2^5. 3^4. 4^3. 5^2

To determine which of these expressions is not a square, we’ll evaluate each one to see if it results in a perfect square (a number that is an integer squared). 

1. \(1^6 = 1\): \(1\) is a perfect square, as \(1 = 1^2\).
2. \(2^5 = 32\): \(32\) is not a perfect square (no integer squared gives \(32\)).
3. \(3^4 = 81\): \(81\) is a perfect square, as \(81 = 9^2\).
4. \(4^3 = 64\): \(64\) is a perfect square, as \(64 = 8^2\).
5. \(5^2 = 25\): \(25\) is a perfect square, as \(25 = 5^2\).

**Conclusion:** \(2^5 = 32\) is not a perfect square.

Would you like a detailed explanation of how I checked each term?

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1. What are the properties of a perfect square?
2. Can a non-square integer power be a perfect square?
3. How does one verify if a number is a perfect square?
4. Are there other powers of integers that yield perfect squares?
5. Why does an odd exponent generally result in a non-square for non-square bases?

**Tip:** When evaluating whether a number is a perfect square, look for an integer that, when squared, gives the original number.

Which of the following is not a square: 1^6, 2^5, 3^4, 4^3, 5^2?

Determine which expression among 1^6, 2^5, 3^4, 4^3, and 5^2 is not a perfect square. Explore key concepts from number theory and exponents, and learn how to verify perfect squares with detailed examples. Suitable for students in Grades 6-8.

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