The number z is irrational. Which statement about sqrt 3 + z is true? Choices: (A)sqrt 3 + z is rational. (B)sqrt 3 + z is irrational. (C)sqrt 3 + z can be rational or irrational, depending on the value of z.

Question

The number z is irrational. Which statement about sqrt 3 + z is true?   Choices: (A)sqrt 3 + z is rational. (B)sqrt 3 + z is irrational. (C)sqrt 3 + z can be rational or irrational, depending on the value of z.

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Identify Type of Number: Identify whether sqrt(3) is a rational or irrational number. The square root of a non-perfect square is an irrational number. sqrt(3) is an irrational number because 3 is not a perfect square.Consider Sum of Irrational Numbers: Consider the sum of two irrational numbers. If z is an irrational number and sqrt(3) is also an irrational number, the sum of two irrational numbers is not necessarily irrational. It can be rational if the irrational parts exactly cancel each other out.Examine Possible Cases: Examine the possible cases for the sum of sqrt(3) and z. If z = -sqrt(3), then sqrt(3) + z = sqrt(3) - sqrt(3) = 0, which is a rational number. If z is any irrational number that is not the negation of sqrt(3), then sqrt(3) + z will be irrational because the sum of an irrational number and a rational number is irrational. Therefore, sqrt(3) + z can be rational or irrational, depending on the value of z.

The number $z$ is irrational. Which statement about $\sqrt{3} + z$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{3} + z$ is rational. $\newline$ (B) $\sqrt{3} + z$ is irrational. $\newline$ (C) $\sqrt{3} + z$ can be rational or irrational, depending on the value of $z$ .

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The number zzz is irrational. Which statement about 3+z\sqrt{3} + z3​+z is true?\newlineChoices:\newline(A) 3+z\sqrt{3} + z3​+z is rational.\newline(B) 3+z\sqrt{3} + z3​+z is irrational.\newline(C) 3+z\sqrt{3} + z3​+z can be rational or irrational, depending on the value of zzz.

The number $z$ is irrational. Which statement about $\sqrt{3} + z$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{3} + z$ is rational. $\newline$ (B) $\sqrt{3} + z$ is irrational. $\newline$ (C) $\sqrt{3} + z$ can be rational or irrational, depending on the value of $z$ .