The number t is rational. Which statement about t - sqrt 17 is true? Choices:[[t - sqrt 17 is rational.][t - sqrt 17 is irrational.][t - sqrt 17 can be rational or irrational, depending on the value of t.]]

Identify Type of Number: Identify whether sqrt(17) is a rational or irrational number. 17 is a non-perfect square. sqrt(17) is an irrational number.17 is Non-Perfect Square: We know: t is a rational number. sqrt(17) is an irrational number. Consider the statement about t - sqrt(17). The subtraction of a rational number (t) and an irrational number (sqrt(17)) will always result in an irrational number.Subtraction Result is Irrational: To confirm, let's consider an example: If t is any rational number, say 1, then 1 - sqrt(17) is not a number that can be expressed as a ratio of two integers, which means it is irrational.

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The number $t$ is rational. Which statement about $t - \sqrt{17}$ is true? $\newline$ Choices: $\newline$ $t - \sqrt{17}$ is rational. $\newline$ $t - \sqrt{17}$ is irrational. $\newline$ $t - \sqrt{17}$ can be rational or irrational, depending on the value of $t$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

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Q. The number

t

is rational. Which statement about

t - \sqrt{17}

is true?

\newline

Choices:

\newline

t - \sqrt{17}

is rational.

\newline

t - \sqrt{17}

is irrational.

\newline

t - \sqrt{17}

can be rational or irrational, depending on the value of

t

Identify Type of Number: Identify whether $\sqrt{17}$ is a rational or irrational number. $17$ is a non-perfect square. $\sqrt{17}$ is an irrational number.
ext{ $17$ is Non-Perfect Square}: We know: $\newline$ $t$ is a rational number. $\newline$ $\sqrt{17}$ is an irrational number. $\newline$ Consider the statement about $t - \sqrt{17}$ . $\newline$ The subtraction of a rational number ( $t$ ) and an irrational number ( $\sqrt{17}$ ) will always result in an irrational number.
Subtraction Result is Irrational: To confirm, let's consider an example: $\newline$ If $t$ is any rational number, say $1$ , then $1 - \sqrt{17}$ is not a number that can be expressed as a ratio of two integers, which means it is irrational.