Let a be a non-zero rational number. Is -sqrt24+a rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (c) It can be either rational or irrational

Evaluate square root of 24: Evaluate the square root of 24. sqrt(24) can be simplified by factoring out perfect squares. sqrt(24) = sqrt(4 * 6) = sqrt(4) * sqrt(6) = 2 * sqrt(6)Nature of sqrt(6): Identify the nature of sqrt(6). sqrt(6) is an irrational number because 6 is not a perfect square, and its square root cannot be expressed as a ratio of two integers.Consider expression -sqrt(24) + a: Consider the expression -sqrt(24) + a. Since we have found that sqrt(24) is 2 * sqrt(6), we can rewrite the expression as -2 * sqrt(6) + a.Nature of expression -2 * sqrt(6) + a: Determine the nature of the expression -2 * sqrt(6) + a. The expression is the sum of an irrational number (-2 * sqrt(6)) and a rational number (a). The sum of a rational and an irrational number is always irrational.Conclusion about expression -sqrt(24) + a: Conclude the nature of the expression -sqrt(24) + a. Since the sum of a rational and an irrational number is irrational, the expression -sqrt(24) + a is irrational.

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Let
a be a non-zero rational number. Is
-sqrt24+a rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(c) It can be either rational or irrational

Let $a$ be a non-zero rational number. Is $-\sqrt{24} + a$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

be a non-zero rational number. Is

-\sqrt{24} + a

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate square root of $24$ : Evaluate the square root of $24$ . $\newline$ $\sqrt{24}$ can be simplified by factoring out perfect squares. $\newline$ $\sqrt{24} = \sqrt{4 \times 6}$ $\newline$ $= \sqrt{4} \times \sqrt{6}$ $\newline$ $= 2 \times \sqrt{6}$
Nature of $\sqrt{6}$ : Identify the nature of $\sqrt{6}$ . $\sqrt{6}$ is an irrational number because $6$ is not a perfect square, and its square root cannot be expressed as a ratio of two integers.
Consider expression $-\sqrt{24} + a$ : Consider the expression $-\sqrt{24} + a$ . $\newline$ Since we have found that $\sqrt{24}$ is $2 \cdot \sqrt{6}$ , we can rewrite the expression as $-2 \cdot \sqrt{6} + a$ .
Nature of expression $-2 \cdot \sqrt{6} + a$ : Determine the nature of the expression $-2 \cdot \sqrt{6} + a$ . $\newline$ The expression is the sum of an irrational number $-2 \cdot \sqrt{6}$ and a rational number $a$ . The sum of a rational and an irrational number is always irrational.
Conclusion about expression $-\sqrt{24} + a$ : Conclude the nature of the expression $-\sqrt{24} + a$ . $\newline$ Since the sum of a rational and an irrational number is irrational, the expression $-\sqrt{24} + a$ is irrational.