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

Analyze Rational Number: Step 1: Analyze choice (A) -3/4. -3/4 is a rational number because it can be expressed as a fraction of two integers.Analyze Irrational Number: Step 2: Analyze choice (B) sqrt(3/4). sqrt(3/4) simplifies to sqrt(3)/2, which is irrational because the square root of 3 is an irrational number.Analyze Repeating Decimal: Step 3: Analyze choice (C) 0.{34}. 0.{34} represents a repeating decimal, which is rational because it can be expressed as a fraction.Analyze Rational Number: Step 4: Analyze choice (D) 3sqrt(4). 3sqrt(4) simplifies to 3*2 = 6, which is a rational number.Analyze Irrational Number: Step 5: Analyze choice (E) sqrt(34). sqrt(34) is an irrational number because 34 is not a perfect square, and its square root cannot be expressed as a fraction.

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

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Select all the numbers that are irrational.

\newline

Multi-select Choices:

\newline

(A)

-\frac{3}{4}

\newline

(B)

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

\newline

(C)

0.\overline{34}

\newline

(D)

3\sqrt{4}

\newline

(E)

\sqrt{34}

Analyze Rational Number: Step $1$ : Analyze choice (A) $-\frac{3}{4}$ . $-\frac{3}{4}$ is a rational number because it can be expressed as a fraction of two integers.
Analyze Irrational Number: Step $2$ : Analyze choice $(B) \sqrt{\frac{3}{4}}$ . $\sqrt{\frac{3}{4}}$ simplifies to $\sqrt{3}/2$ , which is irrational because the square root of $3$ is an irrational number.
Analyze Repeating Decimal: Step $3$ : Analyze choice (C) $0.\overline{34}$ . $0.\overline{34}$ represents a repeating decimal, which is rational because it can be expressed as a fraction.
Analyze Rational Number: Step $4$ : Analyze choice (D) $3\sqrt{4}$ . $3\sqrt{4}$ simplifies to $3\times 2 = 6$ , which is a rational number.
Analyze Irrational Number: Step $5$ : Analyze choice (E) $\sqrt{34}$ . $\sqrt{34}$ is an irrational number because $34$ is not a perfect square, and its square root cannot be expressed as a fraction.