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Which number is closest to $\sqrt{7}$ ? $\newline$ Choices: $\newline$ (A) $2.3$ $\newline$ (B) $1.8$ $\newline$ (C) $2.6$ $\newline$ (D) $2.1$

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Estimate square roots

Full solution

Q. Which number is closest to

\sqrt{7}

?

\newline

Choices:

\newline

(A)

2.3

\newline

(B)

1.8

\newline

(C)

2.6

\newline

(D)

2.1

Identify square roots: Step $1$ : Identify the square roots of the given choices to compare with $\sqrt{7}$ . Calculate $\sqrt{2.3^2}$ , $\sqrt{1.8^2}$ , $\sqrt{2.6^2}$ , and $\sqrt{2.1^2}$ . $2.3^2 = 5.29$ , $1.8^2 = 3.24$ , $2.6^2 = 6.76$ , $2.1^2 = 4.41$ .
Compare with $7$ : Step $2$ : Compare each result with $7$ to find the closest value. $7 - 5.29 = 1.71$ , $7 - 3.24 = 3.76$ , $7 - 6.76 = 0.24$ , $7 - 4.41 = 2.59$ .
Find smallest difference: Step $3$ : Determine which difference is the smallest. $\newline$ The smallest difference is $0.24$ , which corresponds to $2.6$ .

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