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Select all the numbers that are irrational.\newlineMulti-select Choices:\newline(A) 2\sqrt{2}\newline(B) 3\sqrt{3}\newline(C) 5\sqrt{5}\newline(D) 4\sqrt{4}\newline(E) 6\sqrt{6}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Select all the numbers that are irrational.\newlineMulti-select Choices:\newline(A) 2\sqrt{2}\newline(B) 3\sqrt{3}\newline(C) 5\sqrt{5}\newline(D) 4\sqrt{4}\newline(E) 6\sqrt{6}
  1. Understand irrational number definition: Step 11: Understand the definition of an irrational number. An irrational number cannot be expressed as a simple fraction; it's decimal form neither terminates nor repeats.
  2. Evaluate each choice: Step 22: Evaluate each choice:\newline- (A) 2\sqrt{2}: The square root of 22 is known to be irrational because it cannot be expressed as a fraction and its decimal form is non-repeating and non-terminating.\newline- (B) 3\sqrt{3}: Similar to 2\sqrt{2}, 3\sqrt{3} is irrational.\newline- (C) 5\sqrt{5}: This is also an irrational number, following the same reasoning as 2\sqrt{2} and 3\sqrt{3}.\newline- (D) 4\sqrt{4}: This equals 22, which is a rational number because it can be expressed as the fraction 2200.\newline- (E) 2211: Like 2\sqrt{2}, 3\sqrt{3}, and 5\sqrt{5}, 2211 is irrational.

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