The number b is rational. Which statement about b + sqrt 43 is true? Choices: (A)b + sqrt 43 is rational. (B)b + sqrt 43 is irrational. (C)b + sqrt 43 can be rational or irrational, depending on the value of b.

Identify Type of Number: Identify whether sqrt(43) is a rational or irrational number. 43 is a non-perfect square. sqrt(43) is an irrational number.Non-Perfect Square: We know: b is a rational number. sqrt(43) is an irrational number. Consider the sum b + sqrt(43).Sum of Rational and Irrational: The sum of a rational number and an irrational number is always irrational. Therefore, b + sqrt(43) is irrational, regardless of the value of b.

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The number $b$ is rational. Which statement about $b + \sqrt{43}$ is true? $\newline$ Choices: $\newline$ $b + \sqrt{43}$ is rational. $\newline$ $b + \sqrt{43}$ is irrational. $\newline$ $b + \sqrt{43}$ 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{43}

is true?

\newline

Choices:

\newline

b + \sqrt{43}

is rational.

\newline

b + \sqrt{43}

is irrational.

\newline

b + \sqrt{43}

can be rational or irrational, depending on the value of

b

Identify Type of Number: Identify whether $\sqrt{43}$ is a rational or irrational number. $43$ is a non-perfect square. $\sqrt{43}$ is an irrational number.
Non-Perfect Square: We know: $\newline$ $b$ is a rational number. $\newline$ $\sqrt{43}$ is an irrational number. $\newline$ Consider the sum $b + \sqrt{43}$ .
Sum of Rational and Irrational: The sum of a rational number and an irrational number is always irrational. $\newline$ Therefore, $b + \sqrt{43}$ is irrational, regardless of the value of $b$ .