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

Question

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

Bytelearn · Accepted Answer

Simplify sqrt(32): We need to determine the nature of the expression sqrt(32) - v. First, let's simplify sqrt(32). sqrt(32) can be simplified to sqrt(16 * 2), which is sqrt(16) * sqrt(2). Since sqrt(16) is 4 and sqrt(2) is an irrational number, sqrt(32) simplifies to 4 * sqrt(2).Express as 4 * sqrt(2) - v: Now we have the expression 4 * sqrt(2) - v. Since 4 * sqrt(2) is irrational (because sqrt(2) is irrational), and v is also irrational, we need to consider the subtraction of two irrational numbers. The subtraction of two irrational numbers can be either rational or irrational. There is no definitive rule that guarantees the result will be one or the other without knowing the specific values of the irrational numbers.Consider rationality of result: However, since we do not have any specific information about the value of v other than it is irrational, we cannot determine if 4 * sqrt(2) - v will be rational or irrational. The result could be rational if v happens to be exactly 4 * sqrt(2), but in all other cases, it will be irrational. Therefore, without additional information about v, we cannot definitively say that sqrt(32) - v is rational or irrational.

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

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