The number q is irrational. Which statement about q + sqrt 33 is true? Choices: (A)q + sqrt 33 is rational. (B)q + sqrt 33 is irrational. (C)q + sqrt 33 can be rational or irrational, depending on the value of q.

Question

The number q is irrational. Which statement about q + sqrt 33 is true?   Choices: (A)q + sqrt 33 is rational. (B)q + sqrt 33 is irrational. (C)q + sqrt 33 can be rational or irrational, depending on the value of q.

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Identify Type of Number: Identify whether sqrt(33) is a rational or irrational number. 33 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, sqrt(33) is an irrational number.Sum of Irrational Numbers: Consider the sum of two irrational numbers, q and sqrt(33). If q is any irrational number that is not the additive inverse of sqrt(33), then their sum is also irrational. This is because the sum of an irrational number and a rational number is irrational, and the sum of two irrational numbers is generally irrational unless they are additive inverses.Special Cases Consideration: Examine the special cases where q could be the additive inverse of sqrt(33). If q = -sqrt(33), then q + sqrt(33) = -sqrt(33) + sqrt(33) = 0, which is a rational number. This shows that there is at least one value of q for which q + sqrt(33) is rational.Final Conclusion: Determine the correct statement based on the previous steps. Since q + sqrt(33) can be rational if q is the additive inverse of sqrt(33), but is generally irrational for other values of q, the correct statement is that q + sqrt(33) can be rational or irrational, depending on the value of q.

The number $q$ is irrational. Which statement about $q + \sqrt{33}$ is true? $\newline$ Choices: $\newline$ $q + \sqrt{33}$ is rational. $\newline$ $q + \sqrt{33}$ is irrational. $\newline$ $q + \sqrt{33}$ can be rational or irrational, depending on the value of $q$ .

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The number qqq is irrational. Which statement about q+33q + \sqrt{33}q+33​ is true?\newlineChoices:\newline q+33q + \sqrt{33}q+33​ is rational.\newline q+33q + \sqrt{33}q+33​ is irrational.\newline q+33q + \sqrt{33}q+33​ can be rational or irrational, depending on the value of qqq.

The number $q$ is irrational. Which statement about $q + \sqrt{33}$ is true? $\newline$ Choices: $\newline$ $q + \sqrt{33}$ is rational. $\newline$ $q + \sqrt{33}$ is irrational. $\newline$ $q + \sqrt{33}$ can be rational or irrational, depending on the value of $q$ .