Is sqrt 7 a rational number? Choices: (A)yes (B)no

Understand rational number definition: Step 1: Understand the definition of a rational number. A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Evaluate sqrt 7: Step 2: Evaluate sqrt 7. Sqrt 7 is the number that when multiplied by itself gives 7. There is no integer whose square is 7, indicating that sqrt 7 cannot be expressed as a fraction of two integers. Determine decimal type: Step 3: Determine if sqrt 7 is a terminating or repeating decimal. Since sqrt 7 cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal. It is a non-terminating, non-repeating decimal. Conclude sqrt 7 type: Step 4: Conclude if sqrt 7 is rational or irrational. Since sqrt 7 is a non-terminating, non-repeating decimal and cannot be expressed as a fraction of two integers, it is an irrational number.

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Is $\sqrt{7}$ 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{7}

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand rational number definition: Step $1$ : Understand the definition of a rational number. $\newline$ A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
Evaluate $\sqrt{7}$ : Step $2$ : Evaluate $\sqrt{7}$ . $\newline$ $\sqrt{7}$ is the number that when multiplied by itself gives $7$ . $\newline$ There is no integer whose square is $7$ , indicating that $\sqrt{7}$ cannot be expressed as a fraction of two integers.
Determine decimal type: Step $3$ : Determine if $\sqrt{7}$ is a terminating or repeating decimal. Since $\sqrt{7}$ cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal. It is a non-terminating, non-repeating decimal.
Conclude $\sqrt{7}$ type: Step $4$ : Conclude if $\sqrt{7}$ is rational or irrational. $\newline$ Since $\sqrt{7}$ is a non-terminating, non-repeating decimal and cannot be expressed as a fraction of two integers, it is an irrational number.