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Which number is closest to $\sqrt{80}$ ? $\newline$ Choices: $\newline$ (A) $7.9$ $\newline$ (B) $9.4$ $\newline$ (C) $8.9$ $\newline$ (D) $8.4$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{80}

?

\newline

Choices:

\newline

(A)

7.9

\newline

(B)

9.4

\newline

(C)

8.9

\newline

(D)

8.4

Identify Perfect Square Estimate: Step $1$ : Identify a perfect square close to $80$ to estimate the square root. $\newline$ We know $9^2 = 81$ , which is very close to $80$ . So, $\sqrt{80}$ should be slightly less than $9$ .
Compare Squares to $80$ : Step $2$ : Compare the square of the choices to $80$ to find the closest match. $\newline$ (A) $7.9^2 = 62.41$ $\newline$ (B) $9.4^2 = 88.36$ $\newline$ (C) $8.9^2 = 79.21$ $\newline$ (D) $8.4^2 = 70.56$
Determine Closest Match: Step $3$ : Determine which squared value is closest to $80$ . From the calculations: - $62.41$ (A) is far from $80$ . - $88.36$ (B) is higher than $80$ . - $79.21$ (C) is very close to $80$ . - $70.56$ (D) is also far from $80$ . So, $79.21$ is the closest to $80$ .

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