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

Identify Number Nature: Identify the nature of the number 10. 10 is an integer, which is also a rational number.Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. 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 Principle to Problem: Apply this principle to the given problem. Since c is irrational and 10 is rational, c - 10 must also be irrational.

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

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is irrational. Which statement about

c - 10

is true?

\newline

Choices:

\newline

(A)

c - 10

is rational.

\newline

(B)

c - 10

is irrational.

\newline

(C)

c - 10

can be rational or irrational, depending on the value of

c

Identify Number Nature: Identify the nature of the number $10$ . $10$ is an integer, which is also a rational number.
Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. 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 Principle to Problem: Apply this principle to the given problem. $\newline$ Since $c$ is irrational and $10$ is rational, $c - 10$ must also be irrational.