Which lists contain only irrational numbers? Select all that apply. Multi-select Choices: (A)-11.8, -7.3, -9.7, -3, 61.4 (B)sqrt 20, sqrt 50, sqrt 35, sqrt 65, sqrt 70 (C)21/22, 3/11, 1/9, -2/5, -1/17 (D)sqrt 25, sqrt 81, sqrt 36, sqrt 144, sqrt 100 (E)2sqrt 2, 5sqrt 5, 3sqrt 3, 6sqrt 6, 7sqrt 7

Identify Number Nature: Identify the nature of numbers in list (A): -11.8, -7.3, -9.7, -3, 61.4. These are all decimal and whole numbers, which are rational. Examine Square Roots: Examine list (B): sqrt 20, sqrt 50, sqrt 35, sqrt 65, sqrt 70. All numbers are square roots of non-perfect squares, which are irrational. Check Fractions: Check list (C): 21/22, 3/11, 1/9, -2/5, -1/17. These are all fractions, representing rational numbers. Review Perfect Squares: Review list (D): sqrt 25, sqrt 81, sqrt 36, sqrt 144, sqrt 100. These are square roots of perfect squares, which are rational numbers (5, 9, 6, 12, 10 respectively). Analyze Product of Rational: Analyze list (E): 2sqrt 2, 5sqrt 5, 3sqrt 3, 6sqrt 6, 7sqrt 7. Each term is a product of a rational number and the square root of a non-perfect square, making them all irrational.

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Which lists contain only irrational numbers? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $-11.8, -7.3, -9.7, -3, 61.4$ $\newline$ (B) $\sqrt{20}, \sqrt{50}, \sqrt{35}, \sqrt{65}, \sqrt{70}$ $\newline$ (C) $\frac{21}{22}, \frac{3}{11}, \frac{1}{9}, -\frac{2}{5}, -\frac{1}{17}$ $\newline$ (D) $\sqrt{25}, \sqrt{81}, \sqrt{36}, \sqrt{144}, \sqrt{100}$ $\newline$ (E) $2\sqrt{2}, 5\sqrt{5}, 3\sqrt{3}, 6\sqrt{6}, 7\sqrt{7}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

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

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Multi-select Choices:

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(A)

-11.8, -7.3, -9.7, -3, 61.4

\newline

(B)

\sqrt{20}, \sqrt{50}, \sqrt{35}, \sqrt{65}, \sqrt{70}

\newline

(C)

\frac{21}{22}, \frac{3}{11}, \frac{1}{9}, -\frac{2}{5}, -\frac{1}{17}

\newline

(D)

\sqrt{25}, \sqrt{81}, \sqrt{36}, \sqrt{144}, \sqrt{100}

\newline

(E)

2\sqrt{2}, 5\sqrt{5}, 3\sqrt{3}, 6\sqrt{6}, 7\sqrt{7}

Identify Number Nature: Identify the nature of numbers in list $A$ : $-11.8$ , $-7.3$ , $-9.7$ , $-3$ , $61.4$ . These are all decimal and whole numbers, which are rational.
Examine Square Roots: Examine list (B): $\sqrt{20}$ , $\sqrt{50}$ , $\sqrt{35}$ , $\sqrt{65}$ , $\sqrt{70}$ . All numbers are square roots of non-perfect squares, which are irrational.
Check Fractions: Check list (C): $\frac{21}{22}$ , $\frac{3}{11}$ , $\frac{1}{9}$ , $\frac{-2}{5}$ , $\frac{-1}{17}$ . These are all fractions, representing rational numbers.
Review Perfect Squares: Review list (D): $\sqrt{25}$ , $\sqrt{81}$ , $\sqrt{36}$ , $\sqrt{144}$ , $\sqrt{100}$ . These are square roots of perfect squares, which are rational numbers ( $5$ , $9$ , $6$ , $12$ , $10$ respectively).
Analyze Product of Rational: Analyze list $E$ : $2\sqrt{2}$ , $5\sqrt{5}$ , $3\sqrt{3}$ , $6\sqrt{6}$ , $7\sqrt{7}$ . Each term is a product of a rational number and the square root of a non-perfect square, making them all irrational.