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

Evaluate sqrt(3): Evaluate sqrt(3). The square root of a number is a value that, when multiplied by itself, gives the original number. sqrt(3) is the number that when squared gives 3.Identify Rationality: Identify if sqrt(3) can be expressed as a fraction of two integers (the definition of a rational number). sqrt(3) cannot be expressed as a fraction of two integers because there are no two integers whose ratio squared equals 3.Determine Decimal Type: Determine if sqrt(3) is a terminating or repeating decimal. sqrt(3) is known to be a non-terminating, non-repeating decimal, which is a characteristic of irrational numbers.Conclude Number Type: Conclude whether sqrt(3) is a rational or irrational number. Since sqrt(3) cannot be expressed as a fraction of two integers and is a non-terminating, non-repeating decimal, it is an irrational number.

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

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Math Problems

Grade 8

Identify rational and irrational square roots

Full solution

Q. Is

\sqrt{3}

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Evaluate $\sqrt{3}$ : Evaluate $\sqrt{3}$ . The square root of a number is a value that, when multiplied by itself, gives the original number. $\sqrt{3}$ is the number that when squared gives $3$ .
Identify Rationality: Identify if $\sqrt{3}$ can be expressed as a fraction of two integers (the definition of a rational number). $\sqrt{3}$ cannot be expressed as a fraction of two integers because there are no two integers whose ratio squared equals $3$ .
Determine Decimal Type: Determine if $\sqrt{3}$ is a terminating or repeating decimal. $\sqrt{3}$ is known to be a non-terminating, non-repeating decimal, which is a characteristic of irrational numbers.
Conclude Number Type: Conclude whether $\sqrt{3}$ is a rational or irrational number. $\newline$ Since $\sqrt{3}$ cannot be expressed as a fraction of two integers and is a non-terminating, non-repeating decimal, it is an irrational number.