Is sqrt 10 a rational number? Choices: (A)yes (B)no

Define sqrt 10: Step 1: Define sqrt 10. To find if sqrt 10 is rational, we first need to understand what sqrt 10 means. sqrt 10 = the number which when multiplied by itself gives 10.Check if sqrt 10: Step 2: Check if sqrt 10 can be expressed as a fraction of two integers (a/b where a and b are integers and b is not zero). sqrt 10 is not a perfect square, meaning it cannot be expressed as a simple fraction of two integers.Determine decimal type: Step 3: Determine if sqrt 10 is a terminating or repeating decimal. Since sqrt 10 cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal.Conclude rationality: Step 4: Conclude if sqrt 10 is rational or irrational. A rational number can be expressed as a fraction of two integers. Since sqrt 10 cannot be expressed this way, it is an irrational number.

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Is $\sqrt{10}$ 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{10}

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Define $\sqrt{10}$ : Step $1$ : Define $\sqrt{10}$ . $\newline$ To find if $\sqrt{10}$ is rational, we first need to understand what $\sqrt{10}$ means. $\newline$ $\sqrt{10} =$ the number which when multiplied by itself gives $10$ .
Check if $\sqrt{10}$ : Step $2$ : Check if $\sqrt{10}$ can be expressed as a fraction of two integers ( $\frac{a}{b}$ where $a$ and $b$ are integers and $b$ is not zero). $\newline$ $\sqrt{10}$ is not a perfect square, meaning it cannot be expressed as a simple fraction of two integers.
Determine decimal type: Step $3$ : Determine if $\sqrt{10}$ is a terminating or repeating decimal. Since $\sqrt{10}$ cannot be expressed as a fraction of two integers, it is neither a terminating nor a repeating decimal.
Conclude rationality: Step $4$ : Conclude if $\sqrt{10}$ is rational or irrational. $\newline$ A rational number can be expressed as a fraction of two integers. Since $\sqrt{10}$ cannot be expressed this way, it is an irrational number.