3 Answers:
Choice A
Choice D
Choice E
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Explanation:
The list of perfect squares is:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...
If we apply the square root to any of those numbers, then the number is rational.
For example, [tex]\sqrt{25} = 5 = \frac{5}{1}[/tex]
A rational number is any fraction of two integers, where zero is not in the denominator.
Based on this, we can see that choice A represents a rational number because we are summing rational numbers.
More specific proof is to write [tex]\sqrt{4} + \sqrt{16} = 2 + 4 = 6 = \frac{6}{1}[/tex] showing it is rational.
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Choice B is ruled out because [tex]\sqrt{5}[/tex] is irrational. We cannot write it as a fraction of two integers.
Choice C is ruled out for similar reasoning as choice B. This time [tex]\sqrt{24}[/tex] is irrational.
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Choice D is another answer because [tex]2*\sqrt{4} = 2*2 = 4 = \frac{4}{1}[/tex] is rational.
Choice E is another answer as well because [tex]\sqrt{49}*\sqrt{81} = 7*9 = 63 = \frac{63}{1}[/tex] is rational.
Choice F is ruled out because [tex]\sqrt{12}[/tex] is irrational, which in turn makes [tex]3\sqrt{12}[/tex] irrational as well.
