Issqrt 3anirrationalnumber? Choices: (A)yes (B)no

Understand sqrt(3): Step 1: Understand the nature of sqrt(3). Sqrt(3) is the square root of 3, which cannot be expressed as a simple fraction of two integers.Check decimal representation: Step 2: Check if sqrt(3) can be expressed as a terminating or repeating decimal. Since sqrt(3) cannot be expressed as a fraction, it does not have a decimal representation that terminates or repeats.Define irrational numbers: Step 3: Define irrational numbers. An irrational number is a number that cannot be written as a simple fraction, meaning its decimal form is non-terminating and non-repeating.Compare with definition: Step 4: Compare sqrt(3) with the definition of irrational numbers. Since sqrt(3) is non-terminating and non-repeating, it fits the definition of an irrational number.

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Is $\sqrt{3}$ an irrational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Math Problems

Grade 8

Identify rational and irrational numbers

Full solution

Q. Is

\sqrt{3}

an irrational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand $\sqrt{3}$ : Step $1$ : Understand the nature of $\sqrt{3}$ . $\newline$ $\sqrt{3}$ is the square root of $3$ , which cannot be expressed as a simple fraction of two integers.
Check decimal representation: Step $2$ : Check if $\sqrt{3}$ can be expressed as a terminating or repeating decimal. $\newline$ Since $\sqrt{3}$ cannot be expressed as a fraction, it does not have a decimal representation that terminates or repeats.
Define irrational numbers: Step $3$ : Define irrational numbers. An irrational number is a number that cannot be written as a simple fraction, meaning its decimal form is non-terminating and non-repeating.
Compare with definition: Step $4$ : Compare $\sqrt{3}$ with the definition of irrational numbers. $\newline$ Since $\sqrt{3}$ is non-terminating and non-repeating, it fits the definition of an irrational number.