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In the image, the task is to choose the "unlike terms" from the given pairs. To do this, we need to identify pairs of terms that are not identical in their algebraic structure.

1. \( \sqrt{x}; \pi x^{1/2} \)  
   These two terms are like terms because \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and both terms involve the same power of \( x \).

2. \( 5xyz; \sqrt{5xyz} \)  
   These are unlike terms because \( 5xyz \) is a product of variables and constants, while \( \sqrt{5xyz} \) involves a square root, making the powers of the variables different.

3. \( -3abc; 18abc \)  
   These are like terms because they involve the same variables \( abc \) to the same powers, and only their coefficients differ.

4. \( 11\sqrt{xt}; \pi x t^{1/2} \)  
   These are unlike terms because \( 11\sqrt{xt} \) involves \( \sqrt{xt} \), while \( \pi x t^{1/2} \) involves \( t^{1/2} \) but not \( \sqrt{xt} \) exactly.

5. \( 64abc^2; -12abc \)  
   These are unlike terms because \( 64abc^2 \) involves \( c^2 \), while \( -12abc \) involves only \( c \).

Now, we can identify which groups have unlike terms:

- Group 1: Like terms
- Group 2: Unlike terms
- Group 3: Like terms
- Group 4: Unlike terms
- Group 5: Unlike terms

Based on this, the correct answer is the option that includes groups 2, 4, and 5, which is the last option: **2, 4, 5**.

Would you like more details on any part of this explanation?

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**Related questions:**
1. What is the difference between like and unlike terms in algebra?
2. How does the square root affect algebraic terms?
3. Why are the coefficients irrelevant when identifying like terms?
4. Can exponents affect whether terms are like or unlike?
5. How can we simplify expressions involving square roots?

**Tip:** When comparing terms, always check the powers of variables, not just the coefficients, to determine if they are like or unlike terms.

Choose unlike terms from the given pairs of algebraic expressions.

Learn how to identify unlike terms in algebraic expressions by comparing variables, exponents, and coefficients. This problem helps students understand the differences between like and unlike terms, including the effects of exponents and square roots.

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