Let a be a rational number and b be an irrational number. Is a+b rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Properties of Rational and Irrational Numbers: Evaluate the properties of rational and irrational numbers. A rational number can be expressed as the quotient of two integers (a fraction), where the denominator is not zero. An irrational number cannot be expressed as a simple fraction; it has endless non-repeating decimal places.Sum of Rational and Irrational Numbers: Consider the sum of a rational number (a) and an irrational number (b). If a is rational and b is irrational, then their sum cannot be expressed as a simple fraction because the irrational part (b) will still have endless non-repeating decimal places.Concluding the Nature of the Sum: Conclude whether the sum a+b is rational or irrational. Since the irrational part of the sum cannot be eliminated, the sum a+b must be irrational.

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Let
a be a rational number and
b be an irrational number. Is
a+b rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Let $a$ be a rational number and $b$ be an irrational number. Is $a+b$ 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 rational number and

b

be an irrational number. Is

a+b

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Properties of Rational and Irrational Numbers: Evaluate the properties of rational and irrational numbers. $\newline$ A rational number can be expressed as the quotient of two integers (a fraction), where the denominator is not zero. $\newline$ An irrational number cannot be expressed as a simple fraction; it has endless non-repeating decimal places.
Sum of Rational and Irrational Numbers: Consider the sum of a rational number $(a)$ and an irrational number $(b)$ . $\newline$ If $a$ is rational and $b$ is irrational, then their sum cannot be expressed as a simple fraction because the irrational part $(b)$ will still have endless non-repeating decimal places.
Concluding the Nature of the Sum: Conclude whether the sum $a+b$ is rational or irrational. $\newline$ Since the irrational part of the sum cannot be eliminated, the sum $a+b$ must be irrational.