The number w is rational. Which statement about sqrt 22 + w is true? Choices: (A)sqrt 22 + w is rational. (B)sqrt 22 + w is irrational. (C)sqrt 22 + w can be rational or irrational, depending on the value of w.

Identify Type of Number: Identify whether sqrt(22) is a rational or irrational number. 22 is a non-perfect square. sqrt(22) is an irrational number.Nature of Sum: Consider the nature of the sum of a rational number (w) and an irrational number (sqrt(22)). The sum of a rational number and an irrational number is always irrational.Truth of Statements: Determine the truth of the statements given the nature of sqrt(22) and w. Since w is rational and sqrt(22) is irrational, their sum sqrt(22) + w is irrational. Therefore, the correct statement is that sqrt(22) + w is irrational.

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The number $w$ is rational. Which statement about $\sqrt{22} + w$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{22} + w$ is rational. $\newline$ (B) $\sqrt{22} + w$ is irrational. $\newline$ (C) $\sqrt{22} + w$ can be rational or irrational, depending on the value of $w$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

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Q. The number

w

is rational. Which statement about

\sqrt{22} + w

is true?

\newline

Choices:

\newline

(A)

\sqrt{22} + w

is rational.

\newline

(B)

\sqrt{22} + w

is irrational.

\newline

(C)

\sqrt{22} + w

can be rational or irrational, depending on the value of

w

Identify Type of Number: Identify whether $\sqrt{22}$ is a rational or irrational number. $22$ is a non-perfect square. $\sqrt{22}$ is an irrational number.
Nature of Sum: Consider the nature of the sum of a rational number $w$ and an irrational number $\sqrt{22}$ . The sum of a rational number and an irrational number is always irrational.
Truth of Statements: Determine the truth of the statements given the nature of $\sqrt{22}$ and $w$ . Since $w$ is rational and $\sqrt{22}$ is irrational, their sum $\sqrt{22} + w$ is irrational. Therefore, the correct statement is that $\sqrt{22} + w$ is irrational.