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

Analyze sqrt 3/4: Step 1: Analyze (A) sqrt 3/4. sqrt 3/4 can be written as (sqrt 3)/4, which is an irrational number divided by a rational number. The result is irrational.Analyze 3sqrt 4: Step 2: Analyze (B) 3sqrt 4. 3sqrt 4 simplifies to 3*2 = 6, which is a rational number.Analyze -3/4: Step 3: Analyze (C) -3/4. -3/4 is a rational number because it can be expressed as a fraction.Analyze 0.{34}: Step 4: Analyze (D) 0.{34}. 0.{34} represents a repeating decimal, which is rational.Analyze sqrt 34: Step 5: Analyze (E) sqrt 34. sqrt 34 cannot be simplified to a rational number; it's an irrational number.

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

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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.

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Multi-select Choices:

\newline

(A)

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

\newline

(B)

3\sqrt{4}

\newline

(C)

-\frac{3}{4}

\newline

(D)

0.\overline{34}

\newline

(E)

\sqrt{34}

Analyze $\sqrt{\frac{3}{4}}$ : Step $1$ : Analyze (A) $\sqrt{\frac{3}{4}}$ . $\newline$ $\sqrt{\frac{3}{4}}$ can be written as $(\sqrt{3})/4$ , which is an irrational number divided by a rational number. The result is irrational.
Analyze $3\sqrt{4}$ : Step $2$ : Analyze (B) $3\sqrt{4}$ . $3\sqrt{4}$ simplifies to $3\times 2 = 6$ , which is a rational number.
Analyze $-\frac{3}{4}$ : Step $3$ : Analyze (C) $-\frac{3}{4}$ . $\newline$ $-\frac{3}{4}$ is a rational number because it can be expressed as a fraction.
Analyze $0.\overline{34}$ : Step $4$ : Analyze (D) $0.\overline{34}$ . $0.\overline{34}$ represents a repeating decimal, which is rational.
Analyze $\sqrt{34}$ : Step $5$ : Analyze $(E) \sqrt{34}$ . $\newline$ $\sqrt{34}$ cannot be simplified to a rational number; it's an irrational number.