Is sqrt12+4 rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate square root of 12: Evaluate the square root of 12. sqrt(12) = sqrt(4 * 3) = sqrt(4) * sqrt(3) = 2 * sqrt(3)Identify nature of sqrt(3): Identify whether sqrt(3) is a rational or irrational number. sqrt(3) is not a perfect square, and cannot be expressed as a ratio of two integers. Therefore, sqrt(3) is an irrational number.Determine sum of irrational and rational numbers: Determine the nature of the sum of an irrational number and a rational number. Adding a rational number (4) to an irrational number (2 * sqrt(3)) results in an irrational number, because the irrational part cannot be expressed as a ratio of two integers.Conclude nature of sqrt(12) + 4: Conclude whether sqrt(12) + 4 is rational or irrational. Since 2 * sqrt(3) is irrational, and adding 4 (a rational number) to it does not change its irrational nature, sqrt(12) + 4 is irrational.

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Is
sqrt12+4 rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Is $\sqrt{12}+4$ 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. Is

\sqrt{12}+4

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate square root of $12$ : Evaluate the square root of $12$ . $\sqrt{12} = \sqrt{4 \times 3}$ $= \sqrt{4} \times \sqrt{3}$ $= 2 \times \sqrt{3}$
Identify nature of $\sqrt{3}$ : Identify whether $\sqrt{3}$ is a rational or irrational number. $\newline$ $\sqrt{3}$ is not a perfect square, and cannot be expressed as a ratio of two integers. Therefore, $\sqrt{3}$ is an irrational number.
Determine sum of irrational and rational numbers: Determine the nature of the sum of an irrational number and a rational number. $\newline$ Adding a rational number $4$ to an irrational number $2 \times \sqrt{3}$ results in an irrational number, because the irrational part cannot be expressed as a ratio of two integers.
Conclude nature of $\sqrt{12} + 4$ : Conclude whether $\sqrt{12} + 4$ is rational or irrational. $\newline$ Since $2 \cdot \sqrt{3}$ is irrational, and adding $4$ (a rational number) to it does not change its irrational nature, $\sqrt{12} + 4$ is irrational.