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Which number is closest to $\sqrt{23}$ ? $\newline$ Choices: $\newline$ (A) $4.7$ $\newline$ (B) $4.4$ $\newline$ (C) $5.5$ $\newline$ (D) $3.6$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{23}

?

\newline

Choices:

\newline

(A)

4.7

\newline

(B)

4.4

\newline

(C)

5.5

\newline

(D)

3.6

Understand the problem: Step $1$ : Understand the problem. We need to find which number among the choices is closest to the square root of $23$ .
Estimate square root: Step $2$ : Estimate the square root of $23$ . Since $23$ is between the squares of $4$ ( $16$ ) and $5$ ( $25$ ), its square root must be between $4$ and $5$ .
Calculate square root: Step $3$ : Calculate the square root of $23$ using a calculator for more accuracy. $\sqrt{23} \approx 4.7958$ .
Compare with choices: Step $4$ : Compare the calculated square root with the given choices. $\newline$ - Difference with $4.7$ is $|4.7958 - 4.7| = 0.0958$ $\newline$ - Difference with $4.4$ is $|4.7958 - 4.4| = 0.3958$ $\newline$ - Difference with $5.5$ is $|4.7958 - 5.5| = 0.7042$ $\newline$ - Difference with $3.6$ is $|4.7958 - 3.6| = 1.1958$
Determine closest value: Step $5$ : Determine the closest value. The smallest difference is with $4.7$ , so $4.7$ is the closest to the square root of $23$ .

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