Is sqrt23+sqrt77 rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate sqrt(23): Evaluate the nature of sqrt(23) and sqrt(77) individually. sqrt(23) is the square root of a prime number, which cannot be simplified to a fraction of integers. Therefore, sqrt(23) is an irrational number.Evaluate sqrt(77): Similarly, evaluate the nature of sqrt(77). 77 is not a perfect square and cannot be expressed as a fraction of two integers. Therefore, sqrt(77) is also an irrational number.Sum of irrational numbers: Determine the sum of two irrational numbers. The sum of two irrational numbers can be either rational or irrational. However, there is no general rule that guarantees the sum will be rational. In this case, without a specific property that would make the sum rational (such as being additive inverses), we assume the sum remains irrational.Conclude sqrt(23) + sqrt(77): Conclude whether sqrt(23) + sqrt(77) is rational or irrational. Since both sqrt(23) and sqrt(77) are irrational, and there is no evident reason for their sum to be rational, we conclude that sqrt(23) + sqrt(77) is irrational.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Is
sqrt23+sqrt77 rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Is $\sqrt{23} + \sqrt{77}$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

View step-by-step help

Home

Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Is

\sqrt{23} + \sqrt{77}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate $\sqrt{23}$ : Evaluate the nature of $\sqrt{23}$ and $\sqrt{77}$ individually. $\sqrt{23}$ is the square root of a prime number, which cannot be simplified to a fraction of integers. Therefore, $\sqrt{23}$ is an irrational number.
Evaluate $\sqrt{77}$ : Similarly, evaluate the nature of $\sqrt{77}$ . $77$ is not a perfect square and cannot be expressed as a fraction of two integers. Therefore, $\sqrt{77}$ is also an irrational number.
Sum of irrational numbers: Determine the sum of two irrational numbers. $\newline$ The sum of two irrational numbers can be either rational or irrational. However, there is no general rule that guarantees the sum will be rational. In this case, without a specific property that would make the sum rational (such as being additive inverses), we assume the sum remains irrational.
Conclude $\sqrt{23} + \sqrt{77}$ : Conclude whether $\sqrt{23} + \sqrt{77}$ is rational or irrational. $\newline$ Since both $\sqrt{23}$ and $\sqrt{77}$ are irrational, and there is no evident reason for their sum to be rational, we conclude that $\sqrt{23} + \sqrt{77}$ is irrational.