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

Identify Type of Number: Identify whether sqrt(38) is a rational or irrational number. 38 is a non-perfect square, which means that sqrt(38) is an irrational number.Consider Number Properties: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.Apply Property to Problem: Apply the property to the given problem. Since v is rational and sqrt(38) is irrational, sqrt(38) - v will always be irrational.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

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Q. The number

v

is rational. Which statement about

\sqrt{38} - v

is true?

\newline

Choices:

\newline

(A)

\sqrt{38} - v

is rational.

\newline

(B)

\sqrt{38} - v

is irrational.

\newline

(C)

\sqrt{38} - v

can be rational or irrational, depending on the value of

v

Identify Type of Number: Identify whether $\sqrt{38}$ is a rational or irrational number. $38$ is a non-perfect square, which means that $\sqrt{38}$ is an irrational number.
Consider Number Properties: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $v$ is rational and $\sqrt{38}$ is irrational, $\sqrt{38} - v$ will always be irrational.