Select all the numbers that are irrational. Multi-select Choices: (A)sqrt 2 (B)2/3 (C)0.{8} (D) π /2 (E)-4.99

Analyze sqrt(2): Step 1: Analyze the first choice, sqrt(2). Sqrt(2) is known to be an irrational number because it cannot be expressed as a fraction of two integers. Consider 2/3: Step 2: Look at choice (B), which is 2/3. This is a rational number because it is expressed as a fraction where both numerator and denominator are integers. Examine 0.{8}: Step 3: Consider choice (C), which is 0.{8}. This represents the repeating decimal 0.888..., which can be expressed as a fraction (8/9), making it a rational number. Evaluate π/2: Step 4: Evaluate choice (D), π/2. Pi (π) is an irrational number, and dividing it by 2 does not change its nature; thus, π/2 is also irrational. Examine -4.99: Step 5: Examine choice (E), -4.99. This is a decimal number that can be exactly expressed as -499/100, which is a rational number.

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Algebra 2

Simplify rational expressions

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Q. Select all the numbers that are irrational.

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Multi-select Choices:

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(A)

\sqrt{2}

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(B)

\frac{2}{3}

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(C)

0.\overline{8}

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(D)

\frac{\pi}{2}

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(E)

-4.99

Analyze $\sqrt{2}$ : Step $1$ : Analyze the first choice, $\sqrt{2}$ . $\sqrt{2}$ is known to be an irrational number because it cannot be expressed as a fraction of two integers.
Consider $\frac{2}{3}$ : Step $2$ : Look at choice (B), which is $\frac{2}{3}$ . This is a rational number because it is expressed as a fraction where both numerator and denominator are integers.
Examine $0.\overline{8}$ : Step $3$ : Consider choice (C), which is $0.\overline{8}$ . This represents the repeating decimal $0.888\ldots$ , which can be expressed as a fraction $(\frac{8}{9})$ , making it a rational number.
Evaluate $\pi/2$ : Step $4$ : Evaluate choice (D), $\pi/2$ . Pi ( $\pi$ ) is an irrational number, and dividing it by $2$ does not change its nature; thus, $\pi/2$ is also irrational.
Examine $-4.99$ : Step $5$ : Examine choice (E), $-4.99$ . This is a decimal number that can be exactly expressed as $-\frac{499}{100}$ , which is a rational number.