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Select all the rational numbers.\newlineMulti-select Choices:\newline(A) 2\sqrt{2}\newline(B) 64\sqrt{64}\newline(C) 643\sqrt[3]{64}\newline(D) 273\sqrt[3]{27}

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Q. Select all the rational numbers.\newlineMulti-select Choices:\newline(A) 2\sqrt{2}\newline(B) 64\sqrt{64}\newline(C) 643\sqrt[3]{64}\newline(D) 273\sqrt[3]{27}
  1. Define Rational Number: Step 11: Define a rational number.\newlineA rational number can be expressed as the quotient of two integers (a fraction) where the denominator is not zero.
  2. Evaluate 2\sqrt{2}: Step 22: Evaluate Choice (A) 2\sqrt{2}.\newline2\sqrt{2} is known to be an irrational number because it cannot be expressed as a fraction of two integers.
  3. Evaluate 64\sqrt{64}: Step 33: Evaluate Choice (B) 64\sqrt{64}.64=8\sqrt{64} = 8, which is an integer and can be expressed as 81\frac{8}{1}, making it a rational number.
  4. Evaluate 643\sqrt[3]{64}: Step 44: Evaluate Choice (C)(C) 643\sqrt[3]{64}. 643\sqrt[3]{64} equals 44, which is an integer and can be expressed as 41\frac{4}{1}, making it a rational number.
  5. Evaluate 273\sqrt[3]{27}: Step 55: Evaluate Choice (D) 273\sqrt[3]{27}.273=3\sqrt[3]{27} = 3, which is an integer and can be expressed as 31\frac{3}{1}, making it a rational number.

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