The number u is irrational. Which statement about sqrt 45 + u is true? Choices: (A)sqrt 45 + u is rational. (B)sqrt 45 + u is irrational. (C)sqrt 45 + u can be rational or irrational, depending on the value of u.

Question

The number u is irrational. Which statement about sqrt 45 + u is true?   Choices: (A)sqrt 45 + u is rational. (B)sqrt 45 + u is irrational. (C)sqrt 45 + u can be rational or irrational, depending on the value of u.

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Identify Type of Number: Identify whether sqrt(45) is a rational or irrational number. 45 is a non-perfect square, which means that its square root cannot be expressed as a simple fraction of two integers. Therefore, sqrt(45) is an irrational number.Consider Sum with Irrational Number: Consider the sum of two numbers, one of which is irrational. We know that u is an irrational number. We have established that sqrt(45) is also an irrational number. The sum of two irrational numbers is not guaranteed to be irrational; it can be rational or irrational depending on the specific numbers involved.Determine Nature of Sum: Determine the nature of sqrt(45) + u. Since both sqrt(45) and u are irrational, and we cannot determine a specific relationship between them (such as them being additive inverses), we cannot conclude that their sum is rational. Therefore, without additional information about the specific value of u, we must conclude that sqrt(45) + u is irrational.

The number $u$ is irrational. Which statement about $\sqrt{45} + u$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{45} + u$ is rational. $\newline$ (B) $\sqrt{45} + u$ is irrational. $\newline$ (C) $\sqrt{45} + u$ can be rational or irrational, depending on the value of $u$ .

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The number uuu is irrational. Which statement about 45+u\sqrt{45} + u45​+u is true?\newlineChoices:\newline(A) 45+u\sqrt{45} + u45​+u is rational.\newline(B) 45+u\sqrt{45} + u45​+u is irrational.\newline(C) 45+u\sqrt{45} + u45​+u can be rational or irrational, depending on the value of uuu.

The number $u$ is irrational. Which statement about $\sqrt{45} + u$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{45} + u$ is rational. $\newline$ (B) $\sqrt{45} + u$ is irrational. $\newline$ (C) $\sqrt{45} + u$ can be rational or irrational, depending on the value of $u$ .