The number d is irrational. Which statement about sqrt 24 - d is true? Choices: (A)sqrt 24 - d is rational. (B)sqrt 24 - d is irrational. (C)sqrt 24 - d can be rational or irrational, depending on the value of d.

Question

The number d is irrational. Which statement about sqrt 24 - d is true?   Choices: (A)sqrt 24 - d is rational. (B)sqrt 24 - d is irrational. (C)sqrt 24 - d can be rational or irrational, depending on the value of d.

Bytelearn · Accepted Answer

Nature of sqrt(24): First, let's consider the nature of sqrt(24). Sqrt(24) can be simplified to sqrt(4*6), which is 2*sqrt(6). Since sqrt(6) is not a perfect square, it is an irrational number. Therefore, sqrt(24) is irrational.Subtraction of Irrational Numbers: Now, let's consider the subtraction of two numbers: an irrational number (sqrt(24)) and another irrational number (d). The difference between two irrational numbers can be either rational or irrational. However, there is no general rule that guarantees the result will be rational or irrational without knowing the specific values of the two irrational numbers.Indeterminate Result: Since we do not have the specific value of d, we cannot determine the exact nature of sqrt(24) - d. Therefore, without additional information about d, we cannot conclude whether sqrt(24) - d is rational or irrational.Given Choices: Given the choices provided: (A) sqrt(24) - d is rational. (B) sqrt(24) - d is irrational. (C) sqrt(24) - d can be rational or irrational, depending on the value of d. The correct choice is (C) because the nature of the expression depends on the specific value of the irrational number d.

The number $d$ is irrational. Which statement about $\sqrt{24} - d$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{24} - d$ is rational. $\newline$ (B) $\sqrt{24} - d$ is irrational. $\newline$ (C) $\sqrt{24} - d$ can be rational or irrational, depending on the value of $d$ .

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