The number v is irrational. Which statement about v - 10 is true? Choices: (A)v - 10 is rational. (B)v - 10 is irrational. (C)v - 10 can be rational or irrational, depending on the value of v.

Identify Number Nature: Identify the nature of the number 10. 10 is an integer, and all integers are rational numbers.Consider Irrational Number Properties: Consider the properties of irrational numbers. Subtracting a rational number from an irrational number results in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.Apply Property to Problem: Apply the property to the given problem. Since v is irrational and 10 is rational, v - 10 must be irrational.

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The number $v$ is irrational. Which statement about $v - 10$ is true? $\newline$ Choices: $\newline$ (A) $v - 10$ is rational. $\newline$ (B) $v - 10$ is irrational. $\newline$ (C) $v - 10$ 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 irrational. Which statement about

v - 10

is true?

\newline

Choices:

\newline

(A)

v - 10

is rational.

\newline

(B)

v - 10

is irrational.

\newline

(C)

v - 10

can be rational or irrational, depending on the value of

v

Identify Number Nature: Identify the nature of the number $10$ . $10$ is an integer, and all integers are rational numbers.
Consider Irrational Number Properties: Consider the properties of irrational numbers. Subtracting a rational number from an irrational number results in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $v$ is irrational and $10$ is rational, $v - 10$ must be irrational.