Select all the numbers that are irrational. Multi-select Choices: (A)0.{34} (B)sqrt 34 (C)3sqrt 4 (D)-3/4 (E)sqrt 3/4

Analyze option (A): Step 1: Analyze option (A) 0.{34}. 0.{34} represents a repeating decimal, which is not an irrational number because it can be expressed as a fraction.Analyze option (B): Step 2: Analyze option (B) sqrt(34). sqrt(34) cannot be expressed as a fraction of integers and does not have a repeating or terminating decimal expansion, making it an irrational number.Analyze option (C): Step 3: Analyze option (C) 3sqrt(4). 3sqrt(4) simplifies to 3*2 = 6, which is a rational number because it can be expressed as a fraction (6/1).Analyze option (D): Step 4: Analyze option (D) -3/4. -3/4 is a rational number as it is already expressed as a fraction.Analyze option (E): Step 5: Analyze option (E) sqrt(3/4). sqrt(3/4) simplifies to sqrt(3)/2. Since sqrt(3) is an irrational number, dividing it by 2 still results in an irrational number.

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Select all the numbers that are irrational. $\newline$ Multi-select Choices: $\newline$ (A) $0.\overline{34}$ $\newline$ (B) $\sqrt{34}$ $\newline$ (C) $3\sqrt{4}$ $\newline$ (D) $-\frac{3}{4}$ $\newline$ (E) $\sqrt{\frac{3}{4}}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

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Q. Select all the numbers that are irrational.

\newline

Multi-select Choices:

\newline

(A)

0.\overline{34}

\newline

(B)

\sqrt{34}

\newline

(C)

3\sqrt{4}

\newline

(D)

-\frac{3}{4}

\newline

(E)

\sqrt{\frac{3}{4}}

Analyze option (A): Step $1$ : Analyze option (A) $0.\overline{34}$ . $0.\overline{34}$ represents a repeating decimal, which is not an irrational number because it can be expressed as a fraction.
Analyze option (B): Step $2$ : Analyze option (B) $\sqrt{34}$ . $\sqrt{34}$ cannot be expressed as a fraction of integers and does not have a repeating or terminating decimal expansion, making it an irrational number.
Analyze option (C): Step $3$ : Analyze option (C) $3\sqrt{4}$ . $3\sqrt{4}$ simplifies to $3\times 2 = 6$ , which is a rational number because it can be expressed as a fraction $(6/1)$ .
Analyze option (D): Step $4$ : Analyze option (D) $-\frac{3}{4}$ . $-\frac{3}{4}$ is a rational number as it is already expressed as a fraction.
Analyze option (E): Step $5$ : Analyze option (E) $\sqrt{\frac{3}{4}}$ . $\sqrt{\frac{3}{4}}$ simplifies to $\sqrt{3}/2$ . Since $\sqrt{3}$ is an irrational number, dividing it by $2$ still results in an irrational number.