The number t is irrational. Which statement about t + sqrt 27 is true? Choices: (A)t + sqrt 27 is rational. (B)t + sqrt 27 is irrational. (C)t + sqrt 27 can be rational or irrational, depending on the value of t.

Evaluate Square Root of 27: Evaluate the square root of 27. sqrt(27) = sqrt(9 * 3) = sqrt(9) * sqrt(3) = 3 * sqrt(3)Nature of sqrt(3): Identify the nature of sqrt(3). sqrt(3) is an irrational number because it cannot be expressed as a fraction of two integers.Combine Irrational Numbers: Combine the irrational number t with the irrational number 3 * sqrt(3). Since t is irrational and 3 * sqrt(3) is irrational, their sum t + 3 * sqrt(3) is also irrational.Conclude Sum of Irrational Numbers: Conclude the nature of t + sqrt(27). Since t + sqrt(27) is the sum of two irrational numbers, it is irrational.

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The number $t$ is irrational. Which statement about $t + \sqrt{27}$ is true? $\newline$ Choices: $\newline$ (A) $t + \sqrt{27}$ is rational. $\newline$ (B) $t + \sqrt{27}$ is irrational. $\newline$ (C) $t + \sqrt{27}$ can be rational or irrational, depending on the value of $t$ .

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. The number

t

is irrational. Which statement about

t + \sqrt{27}

is true?

\newline

Choices:

\newline

(A)

t + \sqrt{27}

is rational.

\newline

(B)

t + \sqrt{27}

is irrational.

\newline

(C)

t + \sqrt{27}

can be rational or irrational, depending on the value of

t

Evaluate Square Root of $27$ : Evaluate the square root of $27$ . $\newline$ $\sqrt{27} = \sqrt{9 \times 3}$ $\newline$ $= \sqrt{9} \times \sqrt{3}$ $\newline$ $= 3 \times \sqrt{3}$
Nature of $\sqrt{3}$ : Identify the nature of $\sqrt{3}$ . $\newline$ $\sqrt{3}$ is an irrational number because it cannot be expressed as a fraction of two integers.
Combine Irrational Numbers: Combine the irrational number $t$ with the irrational number $3 \times \sqrt{3}$ . Since $t$ is irrational and $3 \times \sqrt{3}$ is irrational, their sum $t + 3 \times \sqrt{3}$ is also irrational.
Conclude Sum of Irrational Numbers: Conclude the nature of $t + \sqrt{27}$ . Since $t + \sqrt{27}$ is the sum of two irrational numbers, it is irrational.