The number b is rational. Which statement about sqrt 44 - b is true? Choices: (A)sqrt 44 - b is rational. (B)sqrt 44 - b is irrational. (C)sqrt 44 - b can be rational or irrational, depending on the value of b.

Identify Non-Perfect Square: We know that the square root of a non-perfect square is irrational. The number 44 is not a perfect square, so sqrt(44) is irrational.Subtract Rational from Irrational: Since b is given to be rational, subtracting a rational number (b) from an irrational number (sqrt(44)) will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.Final Result: Therefore, sqrt(44) - b is irrational, which corresponds to choice (B).

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The number $b$ is rational. Which statement about $\sqrt{44} - b$ is true? $\newline$ Choices: $\newline$ (A) $\sqrt{44} - b$ is rational. $\newline$ (B) $\sqrt{44} - b$ is irrational. $\newline$ (C) $\sqrt{44} - b$ can be rational or irrational, depending on the value of $b$ .

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Math Problems

Precalculus

Properties of operations on rational and irrational numbers

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Q. The number

b

is rational. Which statement about

\sqrt{44} - b

is true?

\newline

Choices:

\newline

(A)

\sqrt{44} - b

is rational.

\newline

(B)

\sqrt{44} - b

is irrational.

\newline

(C)

\sqrt{44} - b

can be rational or irrational, depending on the value of

b

Identify Non-Perfect Square: We know that the square root of a non-perfect square is irrational. The number $44$ is not a perfect square, so $\sqrt{44}$ is irrational.
Subtract Rational from Irrational: Since $b$ is given to be rational, subtracting a rational number ( $b$ ) from an irrational number ( $\sqrt{44}$ ) will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.
Final Result: Therefore, $\sqrt{44} - b$ is irrational, which corresponds to choice (B).