The number q is irrational. Which statement about q + sqrt 18 is true? Choices: (A)q + sqrt 18 is rational. (B)q + sqrt 18 is irrational. (C)q + sqrt 18 can be rational or irrational, depending on the value of q.

Given Information: We are given that q is an irrational number. The square root of 18, sqrt(18), can be simplified to sqrt(9*2) which is 3*sqrt(2). Since sqrt(2) is an irrational number, 3*sqrt(2) is also irrational. The sum of an irrational number and another irrational number is always irrational.Simplifying sqrt(18): Therefore, q + sqrt(18) which is q + 3*sqrt(2) is the sum of two irrational numbers. By the property mentioned earlier, the sum of two irrational numbers is irrational.Sum of Irrational Numbers: The correct statement about q + sqrt(18) is that it is irrational, which corresponds to choice (B).

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The number $q$ is irrational. Which statement about $q + \sqrt{18}$ is true? $\newline$ Choices: $\newline$ (A) $q + \sqrt{18}$ is rational. $\newline$ (B) $q + \sqrt{18}$ is irrational. $\newline$ (C) $q + \sqrt{18}$ can be rational or irrational, depending on the value of $q$ .

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Math Problems

Precalculus

Properties of operations on rational and irrational numbers

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Q. The number

q

is irrational. Which statement about

q + \sqrt{18}

is true?

\newline

Choices:

\newline

(A)

q + \sqrt{18}

is rational.

\newline

(B)

q + \sqrt{18}

is irrational.

\newline

(C)

q + \sqrt{18}

can be rational or irrational, depending on the value of

q

Given Information: We are given that $q$ is an irrational number. The square root of $18$ , $\sqrt{18}$ , can be simplified to $\sqrt{9\times2}$ which is $3\times\sqrt{2}$ . Since $\sqrt{2}$ is an irrational number, $3\times\sqrt{2}$ is also irrational. The sum of an irrational number and another irrational number is always irrational.
Simplifying $\sqrt{18}$ : Therefore, $q + \sqrt{18}$ which is $q + 3\sqrt{2}$ is the sum of two irrational numbers. By the property mentioned earlier, the sum of two irrational numbers is irrational.
Sum of Irrational Numbers: The correct statement about $q + \sqrt{18}$ is that it is irrational, which corresponds to choice $(B)$ .