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Which number is closest to $\sqrt{13}$ ? $\newline$ Choices: $\newline$ (A) $4.2$ $\newline$ (B) $2.8$ $\newline$ (C) $3.6$ $\newline$ (D) $2.9$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{13}

?

\newline

Choices:

\newline

(A)

4.2

\newline

(B)

2.8

\newline

(C)

3.6

\newline

(D)

2.9

Identify Perfect Squares: Step $1$ : Identify the square roots of perfect squares around $13$ to estimate the square root of $13$ . $\newline$ - Square root of $9$ ( $3^2$ ) is $3$ . $\newline$ - Square root of $16$ ( $4^2$ ) is $4$ . $\newline$ Since $13$ is between $9$ and $16$ , $13$ $1$ should be between $3$ and $4$ .
Compare Given Choices: Step $2$ : Compare the given choices to see which is closest to the estimated range of $3$ to $4$ . $\newline$ - Choices are $4.2$ , $2.8$ , $3.6$ , and $2.9$ . $\newline$ - Only $3.6$ and $4.2$ are between $3$ and $4$ .
Calculate Squares: Step $3$ : Calculate the square of $3.6$ and $4.2$ to see which is closer to $13$ . $\newline$ - $(3.6)^2 = 12.96$ $\newline$ - $(4.2)^2 = 17.64$ $\newline$ $12.96$ is closer to $13$ than $17.64$ .

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