The number x is irrational. Which statement about x + sqrt 11 is true? Choices: (A)x + sqrt 11 is rational. (B)x + sqrt 11 is irrational. (C)x + sqrt 11 can be rational or irrational, depending on the value of x.

Question

The number x is irrational. Which statement about x + sqrt 11 is true?   Choices: (A)x + sqrt 11 is rational. (B)x + sqrt 11 is irrational. (C)x + sqrt 11 can be rational or irrational, depending on the value of x.

Bytelearn · Accepted Answer

Identify Type of Number: Identify whether sqrt(11) is a rational or irrational number. 11 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers.Consider Sum of Irrational Numbers: Since sqrt(11) is an irrational number, we need to consider the sum of two irrational numbers, x and sqrt(11). The sum of two irrational numbers can be either rational or irrational, depending on the specific numbers involved.Case: Negative of sqrt(11): Consider the case where x is the negative of sqrt(11). In this case, x + sqrt(11) would equal 0, which is a rational number.Case: x is any Irrational Number: Now consider the case where x is any irrational number that is not the negative of sqrt(11). In this case, x + sqrt(11) would remain irrational, as the sum of an irrational number and a non-identical irrational number is irrational.Conclusion: Since we have found that x + sqrt(11) can be rational in some cases and irrational in others, depending on the value of x, the correct statement is that x + sqrt(11) can be rational or irrational, depending on the value of x.

The number $x$ is irrational. Which statement about $x + \sqrt{11}$ is true? $\newline$ Choices: $\newline$ (A) $x + \sqrt{11}$ is rational. $\newline$ (B) $x + \sqrt{11}$ is irrational. $\newline$ (C) $x + \sqrt{11}$ can be rational or irrational, depending on the value of $x$ .

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