The number b is rational. Which statement about b - sqrt 28 is true? Choices: (A)b - sqrt 28 is rational. (B)b - sqrt 28 is irrational. (C)b - sqrt 28 can be rational or irrational, depending on the value of b.

Identify Type of Number: Identify whether sqrt(28) is a rational or irrational number. 28 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. sqrt(28) is an irrational number.Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational. This is because if the result were rational, adding the irrational number back would yield the original rational number, which contradicts the definition of irrational numbers.Apply Properties: Apply the properties to the given problem. Since b is rational and sqrt(28) is irrational, their difference b - sqrt(28) must be irrational.

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The number $b$ is rational. Which statement about $b - \sqrt{28}$ is true? $\newline$ Choices: $\newline$ (A) $b - \sqrt{28}$ is rational. $\newline$ (B) $b - \sqrt{28}$ is irrational. $\newline$ (C) $b - \sqrt{28}$ can be rational or irrational, depending on the value of $b$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

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Q. The number

b

is rational. Which statement about

b - \sqrt{28}

is true?

\newline

Choices:

\newline

(A)

b - \sqrt{28}

is rational.

\newline

(B)

b - \sqrt{28}

is irrational.

\newline

(C)

b - \sqrt{28}

can be rational or irrational, depending on the value of

b

Identify Type of Number: Identify whether $\sqrt{28}$ is a rational or irrational number. $28$ is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. $\sqrt{28}$ is an irrational number.
Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational. This is because if the result were rational, adding the irrational number back would yield the original rational number, which contradicts the definition of irrational numbers.
Apply Properties: Apply the properties to the given problem. $\newline$ Since $b$ is rational and $\sqrt{28}$ is irrational, their difference $b - \sqrt{28}$ must be irrational.