The number t is irrational. Which statement about t – √47 is true? Choices: [[t – √47 is rational.][t – √47 is irrational.][t – √47 can be rational or irrational, depending on the value of t.]]

Identify Nature of √47: Identify the nature of √47. √47 is the square root of a non-perfect square, which means it is an irrational number.Consider Subtraction of Irrational Numbers: Consider the subtraction of two irrational numbers. The difference between two irrational numbers can be either rational or irrational. It is not possible to determine the nature of t – √47 without knowing the specific value of t.Analyze Given Choices: Analyze the given choices in relation to the subtraction of irrational numbers. If t were specifically chosen to be √47, then t – √47 would be 0, which is rational. However, if t is any other irrational number, t – √47 could still be irrational. Therefore, the statement that t – √47 can be rational or irrational, depending on the value of t, is true.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number $t$ is irrational. Which statement about $t - \sqrt{47}$ is true? $\newline$ Choices: $\newline$ (A) $t - \sqrt{47}$ is rational. $\newline$ (B) $t - \sqrt{47}$ is irrational. $\newline$ (C) $t - \sqrt{47}$ can be rational or irrational, depending on the value of $t$ .

View step-by-step help

Home

Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

t

is irrational. Which statement about

t - \sqrt{47}

is true?

\newline

Choices:

\newline

(A)

t - \sqrt{47}

is rational.

\newline

(B)

t - \sqrt{47}

is irrational.

\newline

(C)

t - \sqrt{47}

can be rational or irrational, depending on the value of

t

Identify Nature of $\sqrt{47}$ : $\sqrt{47}$ is the square root of a non-perfect square, which means it is an irrational number.
Consider Subtraction of Irrational Numbers: Consider the subtraction of two irrational numbers. $\newline$ The difference between two irrational numbers can be either rational or irrational. It is not possible to determine the nature of $t - \sqrt{47}$ without knowing the specific value of $t$ .
Analyze Given Choices: Analyze the given choices in relation to the subtraction of irrational numbers. $\newline$ If $t$ were specifically chosen to be $\sqrt{47}$ , then $t - \sqrt{47}$ would be $0$ , which is rational. $\newline$ However, if $t$ is any other irrational number, $t - \sqrt{47}$ could still be irrational. $\newline$
Final answer: Therefore, the statement that $t - \sqrt{47}$ can be rational or irrational, depending on the value of $t$ , is true.