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Select all the numbers that are irrational.\newlineMulti-select Choices:\newline(A) 39\sqrt{39}\newline(B) 36\sqrt{36}\newline(C) 55\sqrt{55}\newline(D) 40\sqrt{40}\newline(E) 49\sqrt{49}

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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) 39\sqrt{39}\newline(B) 36\sqrt{36}\newline(C) 55\sqrt{55}\newline(D) 40\sqrt{40}\newline(E) 49\sqrt{49}
  1. Check Irrationality of 39\sqrt{39}: Step 11: Determine if 39\sqrt{39} is irrational.\newline39\sqrt{39} cannot be simplified to a perfect square root, meaning it does not result in a whole number. Therefore, it is an irrational number.
  2. Check Irrationality of 36\sqrt{36}: Step 22: Check if 36\sqrt{36} is irrational.\newline36\sqrt{36} equals 66, which is a whole number. Since it can be expressed as a fraction (61\frac{6}{1}), it is not an irrational number.
  3. Check Irrationality of 55\sqrt{55}: Step 33: Evaluate if 55\sqrt{55} is irrational.\newlineLike 39\sqrt{39}, 55\sqrt{55} also cannot be simplified to a perfect square root and does not result in a whole number. Hence, it is an irrational number.
  4. Check Irrationality of 40\sqrt{40}: Step 44: Assess if 40\sqrt{40} is irrational.\newline40\sqrt{40} simplifies to 2⋅102\cdot\sqrt{10}, which is not a whole number. This means it is an irrational number.
  5. Check Irrationality of 49\sqrt{49}: Step 55: Determine if 49\sqrt{49} is irrational.\newline49\sqrt{49} equals 77, which is a whole number. Since it can be expressed as a fraction (7/17/1), it is not an irrational number.

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