The number x is irrational. Which statement about x - sqrt 10 is true? Choices: (A)x - sqrt 10 is rational. (B)x - sqrt 10 is irrational. (C)x - sqrt 10 can be rational or irrational, depending on the value of x.

Question

The number x is irrational. Which statement about x - sqrt 10 is true?   Choices: (A)x - sqrt 10 is rational. (B)x - sqrt 10 is irrational. (C)x - sqrt 10 can be rational or irrational, depending on the value of x.

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Identify Type of Number: Identify whether sqrt(10) is a rational or irrational number. 10 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, sqrt(10) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers when combined with arithmetic operations. The sum or difference of an irrational number and a rational number is always irrational. However, the sum or difference of two irrational numbers can be either rational or irrational, depending on the specific numbers.Apply Properties to Expression: Apply the properties to the given expression x - sqrt(10). Since x is irrational and sqrt(10) is irrational, their difference x - sqrt(10) can be either rational or irrational. For example, if x = sqrt(10), then x - sqrt(10) = sqrt(10) - sqrt(10) = 0, which is rational. If x is any irrational number not related to sqrt(10), then x - sqrt(10) will remain irrational.

The number $x$ is irrational. Which statement about $x - \sqrt{10}$ is true? $\newline$ Choices: $\newline$ (A) $x - \sqrt{10}$ is rational. $\newline$ (B) $x - \sqrt{10}$ is irrational. $\newline$ (C) $x - \sqrt{10}$ can be rational or irrational, depending on the value of $x$ .

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