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Which number is closest to $\sqrt{26}$ ? $\newline$ Choices: $\newline$ (A) $4.5$ $\newline$ (B) $4.7$ $\newline$ (C) $5.0$ $\newline$ (D) $6.5$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{26}

?

\newline

Choices:

\newline

(A)

4.5

\newline

(B)

4.7

\newline

(C)

5.0

\newline

(D)

6.5

Identify perfect squares: Step $1$ : Identify the square roots of perfect squares around $26$ to estimate the square root of $26$ . $\newline$ - $5^2 = 25$ $\newline$ - $6^2 = 36$ $\newline$ Since $26$ is closer to $25$ , the square root of $26$ should be slightly more than $5$ .
Estimate square root: Step $2$ : Compare the given choices to our estimate. $\newline$ - (A) $4.5$ $\newline$ - (B) $4.7$ $\newline$ - (C) $5.0$ $\newline$ - (D) $6.5$ $\newline$ Choice (C) $5.0$ is the closest to our estimated square root, which is just above $5$ .

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