The number t is irrational. Which statement about sqrt 32 - t is true? Choices: (A)sqrt 32 - t is rational. (B)sqrt 32 - t is irrational. (C)sqrt 32 - t can be rational or irrational, depending on the value of t.

Question

The number t is irrational. Which statement about sqrt 32 - t is true?   Choices: (A)sqrt 32 - t is rational. (B)sqrt 32 - t is irrational. (C)sqrt 32 - t can be rational or irrational, depending on the value of t.

Bytelearn · Accepted Answer

Identify Type of Number: Identify whether sqrt(32) is a rational or irrational number. 32 is a perfect square of 4 times 8, which means sqrt(32) = sqrt(4 * 8) = sqrt(4) * sqrt(8) = 2 * sqrt(8). Since sqrt(8) is not a perfect square, it is irrational. Therefore, sqrt(32) is irrational.Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational. For example, if t = sqrt(32), then sqrt(32) - t = 0, which is rational. However, if t is any other irrational number, then sqrt(32) - t is likely to be irrational.Determine Always True Statement: Determine the statement that is always true. Since sqrt(32) - t can be rational if t = sqrt(32), but is irrational for any other irrational t, the correct statement is that sqrt(32) - t can be rational or irrational, depending on the value of t.

The number $t$ is irrational. Which statement about $\sqrt{32} - t$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{32} - t$ is rational. $\newline$ (B) $\sqrt{32} - t$ is irrational. $\newline$ (C) $\sqrt{32} - t$ can be rational or irrational, depending on the value of $t$ .

Full solution

More problems from Properties of operations on rational and irrational numbers

Related topics