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

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

b

is irrational. Which statement about

b - 9

is true?

\newline

Choices:

\newline

(A)

b - 9

is rational.

\newline

(B)

b - 9

is irrational.

\newline

(C)

b - 9

can be rational or irrational, depending on the value of

b

.

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a perfect square and can be expressed as $3^2$ .Therefore, $9$ is a rational number.
Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. If $b$ is an irrational number and $9$ is a rational number, then $b - 9$ is the subtraction of a rational number from an irrational number. The result of subtracting a rational number from an irrational number is always irrational.
Conclude Nature of $b - 9$ : Conclude the nature of $b - 9$ . $\newline$ Since $b$ is irrational and $9$ is rational, $b - 9$ must be irrational. $\newline$ Therefore, the correct statement about $b - 9$ is that it is irrational.

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t - \sqrt{47}

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