The number v is rational. Which statement about v - sqrt 14 is true? Choices: (A)v - sqrt 14 is rational. (B)v - sqrt 14 is irrational. (C)v - sqrt 14 can be rational or irrational, depending on the value of v.

Identify Type of Number: Identify whether sqrt(14) is a rational or irrational number. 14 is a non-perfect square. sqrt(14) is an irrational number.Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.Apply Property: Apply the property to the given problem. Since v is rational and sqrt(14) is irrational, v - sqrt(14) must be irrational.

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The number $v$ is rational. Which statement about $v - \sqrt{14}$ is true? $\newline$ Choices: $\newline$ (A) $v - \sqrt{14}$ is rational. $\newline$ (B) $v - \sqrt{14}$ is irrational. $\newline$ (C) $v - \sqrt{14}$ can be rational or irrational, depending on the value of $v$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

v

is rational. Which statement about

v - \sqrt{14}

is true?

\newline

Choices:

\newline

(A)

v - \sqrt{14}

is rational.

\newline

(B)

v - \sqrt{14}

is irrational.

\newline

(C)

v - \sqrt{14}

can be rational or irrational, depending on the value of

v

Identify Type of Number: Identify whether $\sqrt{14}$ is a rational or irrational number. $14$ is a non-perfect square. $\sqrt{14}$ is an irrational number.
Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.
Apply Property: Apply the property to the given problem. $\newline$ Since $v$ is rational and $\sqrt{14}$ is irrational, $v - \sqrt{14}$ must be irrational.