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Is $\sqrt{10}$ a natural number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Classify numbers

Full solution

Q. Is

\sqrt{10}

a natural number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Define Natural Numbers: Understand what a natural number is. $\newline$ Natural numbers are the set of positive integers starting from $1$ , $2$ , $3$ , and so on. They do not include fractions, decimals, or negative numbers.
Calculate Square Root of $10$ : Consider the square root of $10$ . The square root of $10$ ( $\sqrt{10}$ ) is the number which when multiplied by itself gives the product $10$ .
Determine if $\sqrt{10}$ is Natural: Determine if $\sqrt{10}$ is a natural number. $\newline$ We know that the square root of $9$ is $3$ and the square root of $16$ is $4$ . Since $10$ is between $9$ and $16$ , the square root of $10$ must be between $3$ and $4$ . Therefore, it cannot be a natural number because natural numbers are whole numbers and $\sqrt{10}$ is not a whole number.

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