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Which number is closest to $\sqrt{13}$ ? $\newline$ Choices: $\newline$ (A) $3.6$ $\newline$ (B) $2.9$ $\newline$ (C) $3.1$ $\newline$ (D) $3.2$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{13}

?

\newline

Choices:

\newline

(A)

3.6

\newline

(B)

2.9

\newline

(C)

3.1

\newline

(D)

3.2

Understand the problem: Step $1$ : Understand the problem. We need to find which number among the choices is closest to the square root of $13$ .
Calculate square root: Step $2$ : Calculate the square root of $13$ using a calculator for accuracy. $\sqrt{13} \approx 3.605551275$ .
Compare with choices: Step $3$ : Compare the calculated square root with the given choices. $\newline$ - Difference with (A) $3.6$ is $|3.605551275 - 3.6| = 0.005551275$ $\newline$ - Difference with (B) $2.9$ is $|3.605551275 - 2.9| = 0.705551275$ $\newline$ - Difference with (C) $3.1$ is $|3.605551275 - 3.1| = 0.505551275$ $\newline$ - Difference with (D) $3.2$ is $|3.605551275 - 3.2| = 0.405551275$
Identify smallest difference: Step $4$ : Identify the smallest difference. The smallest difference is with choice (A) $3.6$ .

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