A) [tex]-\sqrt{5}[/tex]
D) [tex]\pi[/tex]
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Explanation:
Choices B and C are rational because we can simplify them to form a fraction of integers.
[tex]-\sqrt{49} = -7 = -\frac{7}{1}[/tex]
[tex]\sqrt{0} = 0 = \frac{0}{1}[/tex]
Any rational number is of the form P/Q where P,Q are integers and Q is nonzero.
So we can rule out choices B and C.
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Choice A on the other hand cannot be written as a fraction of integers. The 5 isn't a perfect square, which makes [tex]-\sqrt{5}[/tex] irrational.
The same can be said about [tex]\pi[/tex] which is roughly equal to 3.14; the decimal digits go on forever without a known pattern.
Choice A and choice D are the two answers.
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If we know the pattern of the decimal digits, then we can turn the decimal number into a fraction of integers
The number -0.777, where the 7s go on forever, converts to the fraction -7/9
That means we rule out choice E.