Which lists contain only irrational numbers? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $\sqrt{80}, \sqrt{90}, \sqrt{110}, \sqrt{120}, \sqrt{140}$ $\newline$ (B) $\sqrt{25}, \sqrt{64}, \sqrt{81}, \sqrt{49}, \sqrt{36}$ $\newline$ (C) $0.\overline{7}, 0.\overline{9}, 0.\overline{1}, 0.\overline{3}, 0.\overline{5}$ $\newline$ (D) $-7, -9, -11, -3, -5$ $\newline$ (E) $\sqrt{18}, \sqrt{14}, \sqrt{12}, \sqrt{24}, \sqrt{32}$

Full solution

Q. Which lists contain only irrational numbers? Select all that apply.

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Multi-select Choices:

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(A)

\sqrt{80}, \sqrt{90}, \sqrt{110}, \sqrt{120}, \sqrt{140}

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(B)

\sqrt{25}, \sqrt{64}, \sqrt{81}, \sqrt{49}, \sqrt{36}

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(C)

0.\overline{7}, 0.\overline{9}, 0.\overline{1}, 0.\overline{3}, 0.\overline{5}

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(D)

-7, -9, -11, -3, -5

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(E)

\sqrt{18}, \sqrt{14}, \sqrt{12}, \sqrt{24}, \sqrt{32}

Identify Number Nature: Step $1$ : Identify the nature of numbers in each list. $\newline$ - List A: $\sqrt{80}$ , $\sqrt{90}$ , $\sqrt{110}$ , $\sqrt{120}$ , $\sqrt{140}$ . All these numbers are square roots of non-perfect squares, which are irrational.
Check List B: Step $2$ : Check List B: $\sqrt{25}$ , $\sqrt{64}$ , $\sqrt{81}$ , $\sqrt{49}$ , $\sqrt{36}$ . These are all square roots of perfect squares, which are rational numbers.
Examine List C: Step $3$ : Examine List C: $0.\overline{7}$ , $0.\overline{9}$ , $0.\overline{1}$ , $0.\overline{3}$ , $0.\overline{5}$ . These are repeating decimals, which are rational numbers.
Analyze List D: Step $4$ : Analyze List D: $-7$ , $-9$ , $-11$ , $-3$ , $-5$ . These are all integers, and integers are rational numbers.
Review List E: Step $5$ : Review List E: $\sqrt{18}$ , $\sqrt{14}$ , $\sqrt{12}$ , $\sqrt{24}$ , $\sqrt{32}$ . Similar to List A, these are square roots of non-perfect squares, which are irrational.