The number w is irrational. Which statement about w - sqrt 5 is true? Choices: (A)w - sqrt 5 is rational. (B)w - sqrt 5 is irrational. (C)w - sqrt 5 can be rational or irrational, depending on the value of w.

Identify Type of Number: Identify whether sqrt(5) is a rational or irrational number. 5 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, sqrt(5) is an irrational number.Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be either rational or irrational. It depends on the specific numbers involved. For example: - If w = sqrt(5), then w - sqrt(5) = sqrt(5) - sqrt(5) = 0, which is rational. - If w is any irrational number not related to sqrt(5), then w - sqrt(5) is likely to be irrational because the difference of two unrelated irrational numbers is typically irrational. Therefore, without additional information about w, we cannot definitively say whether w - sqrt(5) is rational or irrational.

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The number $w$ is irrational. Which statement about $w - \sqrt{5}$ is true? $\newline$ Choices: $\newline$ (A) $w - \sqrt{5}$ is rational. $\newline$ (B) $w - \sqrt{5}$ is irrational. $\newline$ (C) $w - \sqrt{5}$ can be rational or irrational, depending on the value of $w$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

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Q. The number

w

is irrational. Which statement about

w - \sqrt{5}

is true?

\newline

Choices:

\newline

(A)

w - \sqrt{5}

is rational.

\newline

(B)

w - \sqrt{5}

is irrational.

\newline

(C)

w - \sqrt{5}

can be rational or irrational, depending on the value of

w

Identify Type of Number: Identify whether $\sqrt{5}$ is a rational or irrational number. $5$ is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. Therefore, $\sqrt{5}$ is an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be either rational or irrational. It depends on the specific numbers involved. For example: - If $w = \sqrt{5}$ , then $w - \sqrt{5} = \sqrt{5} - \sqrt{5} = 0$ , which is rational. - If $w$ is any irrational number not related to $\sqrt{5}$ , then $w - \sqrt{5}$ is likely to be irrational because the difference of two unrelated irrational numbers is typically irrational. Therefore, without additional information about $w$ , we cannot definitively say whether $w - \sqrt{5}$ is rational or irrational.