The number b is rational. Which statement about b - sqrt 3 is true? Choices: (A)b - sqrt 3 is rational. (B)b - sqrt 3 is irrational. (C)b - sqrt 3 can be rational or irrational, depending on the value of b.

Identify Type of Number: Identify whether sqrt(3) is a rational or irrational number. Since 3 is a non-perfect square, sqrt(3) 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.Apply Property: Apply the property to the given problem. Since b is rational and sqrt(3) is irrational, b - sqrt(3) must be irrational.

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The number $b$ is rational. Which statement about $b - \sqrt{3}$ is true? $\newline$ Choices: $\newline$ (A) $b - \sqrt{3}$ is rational. $\newline$ (B) $b - \sqrt{3}$ is irrational. $\newline$ (C) $b - \sqrt{3}$ 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

Full solution

Q. The number

b

is rational. Which statement about

b - \sqrt{3}

is true?

\newline

Choices:

\newline

(A)

b - \sqrt{3}

is rational.

\newline

(B)

b - \sqrt{3}

is irrational.

\newline

(C)

b - \sqrt{3}

can be rational or irrational, depending on the value of

b

Identify Type of Number: Identify whether $\sqrt{3}$ is a rational or irrational number. $\newline$ Since $3$ is a non-perfect square, $\sqrt{3}$ 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.
Apply Property: Apply the property to the given problem. $\newline$ Since $b$ is rational and $\sqrt{3}$ is irrational, $b - \sqrt{3}$ must be irrational.