The number y is irrational. Which statement about y - 9 is true? Choices: (A)y - 9 is rational. (B)y - 9 is irrational. (C)y - 9 can be rational or irrational, depending on the value of y.

Identify Number 9: Identify the nature of the number 9. 9 is a perfect square and its square root is 3. Therefore, 9 is 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 will result 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 Rule to Problem: Apply this rule to the given problem. Since y is irrational and 9 is rational, y - 9 will be irrational.

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The number $y$ is irrational. Which statement about $y - 9$ is true? $\newline$ Choices: $\newline$ (A) $y - 9$ is rational. $\newline$ (B) $y - 9$ is irrational. $\newline$ (C) $y - 9$ can be rational or irrational, depending on the value of $y$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is irrational. Which statement about

y - 9

is true?

\newline

Choices:

\newline

(A)

y - 9

is rational.

\newline

(B)

y - 9

is irrational.

\newline

(C)

y - 9

can be rational or irrational, depending on the value of

y

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a perfect square and its square root is $3$ . Therefore, $9$ is 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 will result 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 Rule to Problem: Apply this rule to the given problem. $\newline$ Since $y$ is irrational and $9$ is rational, $y - 9$ will be irrational.