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

Question

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

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Identify Number Type: Identify whether sqrt(33) is a rational or irrational number. 33 is a non-perfect square. sqrt(33) is an irrational number.Consider Sum of Irrational Numbers: Consider the sum of two irrational numbers. We know: b is an irrational number. sqrt(33) is an irrational number. The sum of two irrational numbers is not necessarily irrational. For example, if b = -sqrt(33), then sqrt(33) + b = sqrt(33) - sqrt(33) = 0, which is rational.Determine Nature of Sum: Determine the possible nature of sqrt(33) + b. If b is any irrational number other than -sqrt(33), then sqrt(33) + b will be irrational because the sum of an irrational number and a rational number is irrational. However, if b = -sqrt(33), then sqrt(33) + b is rational. Therefore, sqrt(33) + b can be rational or irrational, depending on the value of b.

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

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The number bbb is irrational. Which statement about 33+b\sqrt{33} + b33​+b is true?\newlineChoices:\newline(A)33+b\sqrt{33} + b33​+b is rational.\newline(B)33+b\sqrt{33} + b33​+b is irrational.\newline(C)33+b\sqrt{33} + b33​+b can be rational or irrational, depending on the value of bbb.

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