The number c is irrational. Which statement about 3+c is true? a) 3+c is rational. b) 3+c is irrational. c) 3+c can be rational or irrational, depending on the value of c.

Understand Number 3: Step 1: Understand the nature of the number 3. 3 is a rational number, as it can be expressed as a fraction 3/1.Analyze Sum: Step 2: Analyze the sum of a rational and an irrational number. Adding a rational number (3) to an irrational number (c) results in an irrational number. This is because the sum of a rational and an irrational number is always irrational.Conclude Nature: Step 3: Conclude the nature of 3+c. Since 3 is rational and c is irrational, their sum 3+c is irrational.

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The number c is irrational. Which statement about 3+c is true?

a) 3+c is rational.

b) 3+c is irrational.

c) 3+c can be rational or irrational, depending on the value of c.

The number $c$ is irrational. Which statement about $3+c$ is true? $\newline$ a) $3+c$ is rational. $\newline$ b) $3+c$ is irrational. $\newline$ c) $3+c$ can be rational or irrational, depending on the value of $c$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is irrational. Which statement about

3+c

is true?

\newline

3+c

is rational.

\newline

3+c

is irrational.

\newline

3+c

can be rational or irrational, depending on the value of

c

Understand Number $3$ : Step $1$ : Understand the nature of the number $3$ . $3$ is a rational number, as it can be expressed as a fraction $\frac{3}{1}$ .
Analyze Sum: Step $2$ : Analyze the sum of a rational and an irrational number. $\newline$ Adding a rational number $3$ to an irrational number $c$ results in an irrational number. This is because the sum of a rational and an irrational number is always irrational.
Conclude Nature: Step $3$ : Conclude the nature of $3+c$ . Since $3$ is rational and $c$ is irrational, their sum $3+c$ is irrational.