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

Question

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

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 sum of an irrational number and a rational number is irrational. The sum of two irrational numbers can be either rational or irrational, depending on the numbers.Analyze Given Statements: Analyze the given statements with respect to the properties of irrational numbers. If s is an irrational number that is not specifically related to sqrt(38), then sqrt(38) + s is likely to be irrational. However, if s is chosen such that it is the negative of sqrt(38), then sqrt(38) + s would be 0, which is rational. Therefore, sqrt(38) + s can be rational or irrational, depending on the value of s.

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

Full solution

More problems from Properties of operations on rational and irrational numbers

Related topics

The number sss is irrational. Which statement about 38+s\sqrt{38} + s38​+s is true?\newlineChoices:\newline(A) 38+s\sqrt{38} + s38​+s is rational.\newline(B) 38+s\sqrt{38} + s38​+s is irrational.\newline(C) 38+s\sqrt{38} + s38​+s can be rational or irrational, depending on the value of sss.

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