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Which two integers is $–\sqrt{91}$ between? $\newline$ Choices: $\newline$ (A) $–10$ and $–9$ $\newline$ (B) $–7$ and $–6$ $\newline$ (C) $–8$ and $–7$ $\newline$ (D) $–11$ and $–10$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{91}

between?

\newline

Choices:

\newline

(A)

–10

and

–9

\newline

(B)

–7

and

–6

\newline

(C)

–8

and

–7

\newline

(D)

–11

and

–10

Identify Perfect Squares: Calculate the approximate value of $\sqrt{91}$ by identifying the nearest perfect squares. $\newline$ Perfect squares near $91$ are $81$ ( $9^2$ ) and $100$ ( $10^2$ ).
Calculate Square Roots: Calculate the square roots of $81$ and $100$ . $\sqrt{81} = 9$ $\sqrt{100} = 10$
Determine Negative Square Roots: Determine the negative square roots since the problem asks for $-\sqrt{91}$ .
$-\sqrt{81} = -9$
$-\sqrt{100} = -10$
Place Negative Square Root: Place $-\sqrt{91}$ between the two calculated negative square roots. $\newline$ $-10 < -\sqrt{91} < -9$

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