The number q is irrational. Which statement about q - sqrt 39 is true? Choices: (A)q - sqrt 39 is rational. (B)q - sqrt 39 is irrational. (C)q - sqrt 39 can be rational or irrational, depending on the value of q.

Identify Type of Number: Identify whether sqrt(39) is a rational or irrational number. 39 is a non-perfect square. sqrt(39) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum or difference of a rational number and an irrational number is always irrational. The sum or difference of two irrational numbers can be rational or irrational.Analyze Expressions with Scenarios: Analyze the given expressions with different scenarios. If q is an irrational number not related to sqrt(39), then q - sqrt(39) would be irrational. If q = sqrt(39), then sqrt(39) - sqrt(39) = 0, which is rational. Therefore, q - sqrt(39) can be rational or irrational, depending on the value of q.

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The number $q$ is irrational. Which statement about $q - \sqrt{39}$ is true? $\newline$ Choices: $\newline$ (A) $q - \sqrt{39}$ is rational. $\newline$ (B) $q - \sqrt{39}$ is irrational. $\newline$ (C) $q - \sqrt{39}$ can be rational or irrational, depending on the value of $q$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

q

is irrational. Which statement about

q - \sqrt{39}

is true?

\newline

Choices:

\newline

(A)

q - \sqrt{39}

is rational.

\newline

(B)

q - \sqrt{39}

is irrational.

\newline

(C)

q - \sqrt{39}

can be rational or irrational, depending on the value of

q

Identify Type of Number: Identify whether $\sqrt{39}$ is a rational or irrational number. $39$ is a non-perfect square. $\sqrt{39}$ is an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum or difference of a rational number and an irrational number is always irrational. The sum or difference of two irrational numbers can be rational or irrational.
Analyze Expressions with Scenarios: Analyze the given expressions with different scenarios. $\newline$ If $q$ is an irrational number not related to $\sqrt{39}$ , then $q - \sqrt{39}$ would be irrational. $\newline$ If $q = \sqrt{39}$ , then $\sqrt{39} - \sqrt{39} = 0$ , which is rational. $\newline$ Therefore, $q - \sqrt{39}$ can be rational or irrational, depending on the value of $q$ .