The number y is irrational. Which statement about y - sqrt 38 is true? Choices: (A)y - sqrt 38 is rational. (B)y - sqrt 38 is irrational. (C)y - sqrt 38 can be rational or irrational, depending on the value of y.

Question

The number y is irrational. Which statement about y - sqrt 38 is true?   Choices: (A)y - sqrt 38 is rational. (B)y - sqrt 38 is irrational. (C)y - sqrt 38 can be rational or irrational, depending on the value of y.

Bytelearn · Accepted Answer

Identify Type of Number: Identify whether sqrt(38) is a rational or irrational number. 38 is a non-perfect square. sqrt(38) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational.Specific Case Analysis: Analyze the specific case where y = sqrt(38). If y = sqrt(38), then y - sqrt(38) = sqrt(38) - sqrt(38) = 0, which is a rational number.Analysis of Different Cases: Analyze the specific case where y is any irrational number not equal to sqrt(38). If y is not equal to sqrt(38), then y - sqrt(38) is the difference of two distinct irrational numbers, which is generally irrational.Conclusion: Conclude that y - sqrt(38) can be rational or irrational, depending on the value of y. If y is chosen specifically to be sqrt(38), the result is rational. Otherwise, it is typically irrational.

The number $y$ is irrational. Which statement about $y - \sqrt{38}$ is true? $\newline$ Choices: $\newline$ (A) $y - \sqrt{38}$ is rational. $\newline$ (B) $y - \sqrt{38}$ is irrational. $\newline$ (C) $y - \sqrt{38}$ can be rational or irrational, depending on the value of $y$ .

Full solution

More problems from Properties of operations on rational and irrational numbers

Related topics