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Which of the following are irrational numbers?\newlineMulti-select Choices:\newline(A) 77\newline(B) 22\newline(C) 7\sqrt{7}\newline(D) 00

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Q. Which of the following are irrational numbers?\newlineMulti-select Choices:\newline(A) 77\newline(B) 22\newline(C) 7\sqrt{7}\newline(D) 00
  1. Definition of Irrational Numbers: An irrational number is a number that cannot be expressed as a simple fraction. Irrational numbers have endless non-repeating decimals. To determine if the given numbers are irrational, we need to check if they can be expressed as a fraction or if they have a non-repeating, non-terminating decimal expansion.
  2. Checking Number (A)7(A) 7: (A)7(A) 7 is an integer, and all integers can be expressed as a fraction with a denominator of 11 (for example, 77 can be written as 71\frac{7}{1}). Therefore, 77 is not an irrational number.
  3. Checking Number BB 22: BB 22 is also an integer, and like 77, it can be expressed as a fraction 21\frac{2}{1}. Therefore, 22 is not an irrational number.
  4. Checking Number (C)7(C) 7: (C)7(C) 7 is listed again, and as previously stated, it is not an irrational number because it can be expressed as a fraction 71\frac{7}{1}.
  5. Checking Number (D)0(D) 0: (D)0(D) 0 is an integer and can be expressed as a fraction 01\frac{0}{1}. Therefore, 00 is not an irrational number.
  6. Conclusion: Since none of the given numbers (A)7,(B)2,(C)7,(A) 7, (B) 2, (C) 7, and (D)0(D) 0 are irrational, the correct answer is that none of the choices are irrational numbers.

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