The number t is irrational. Which statement about sqrt 3 - t is true? Choices: (A)sqrt 3 - t is rational. (B)sqrt 3 - t is irrational. (C)sqrt 3 - t can be rational or irrational, depending on the value of t.

Identify Type of Number: Identify whether sqrt(3) is a rational or irrational number. Since 3 is not a perfect square, sqrt(3) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational, depending on the specific values of those numbers.Analysis of Given Statements: Analyze the given statements with respect to the properties of irrational numbers. If t = sqrt(3), then sqrt(3) - sqrt(3) = 0, which is rational. If t is any irrational number other than sqrt(3), then sqrt(3) - t is irrational because the difference of two distinct irrational numbers is irrational. Therefore, sqrt(3) - t can be rational or irrational, depending on the value of t.

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The number $t$ is irrational. Which statement about $\sqrt{3} - t$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{3} - t$ is rational. $\newline$ (B) $\sqrt{3} - t$ is irrational. $\newline$ (C) $\sqrt{3} - t$ 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

Full solution

Q. The number

t

is irrational. Which statement about

\sqrt{3} - t

is true?

\newline

Choices:

\newline

(A)

\sqrt{3} - t

is rational.

\newline

(B)

\sqrt{3} - t

is irrational.

\newline

(C)

\sqrt{3} - t

can be rational or irrational, depending on the value of

t

Identify Type of Number: Identify whether $\sqrt{3}$ is a rational or irrational number. $\newline$ Since $3$ is not a perfect square, $\sqrt{3}$ is an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational, depending on the specific values of those numbers.
Analysis of Given Statements: Analyze the given statements with respect to the properties of irrational numbers. $\newline$ If $t = \sqrt{3}$ , then $\sqrt{3} - \sqrt{3} = 0$ , which is rational. $\newline$ If $t$ is any irrational number other than $\sqrt{3}$ , then $\sqrt{3} - t$ is irrational because the difference of two distinct irrational numbers is irrational. $\newline$ Therefore, $\sqrt{3} - t$ can be rational or irrational, depending on the value of $t$ .