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Which two integers is $–\sqrt{117}$ between? $\newline$ Choices: $\newline$ (A) $–9$ and $–8$ $\newline$ (B) $–11$ and $–10$ $\newline$ (C) $8$ and $9$ $\newline$ (D) $10$ and $11$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{117}

between?

\newline

Choices:

\newline

(A)

–9

and

–8

\newline

(B)

–11

and

–10

\newline

(C)

8

and

9

\newline

(D)

10

and

11

Identify Perfect Squares: Identify the perfect squares around $117$ . The perfect square just below $117$ is $100$ ( $10^2$ ). The perfect square just above $117$ is $121$ ( $11^2$ ).
Calculate Square Roots: Calculate the square roots of these perfect squares. $\newline$ $\sqrt{100} = 10$ . $\newline$ $\sqrt{121} = 11$ .
Determine Negative Roots: Determine the negative square roots. $\newline$ $-\sqrt{100} = -10.$ $\newline$ $-\sqrt{121} = -11.$
Place Negative Square Root: Place $-\sqrt{117}$ in the correct interval. $\newline$ Since $-11 < -\sqrt{117} < -10$ , $-\sqrt{117}$ is between $-11$ and $-10$ .

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