Which two integers is –sqrt 117 between? Choices: (A)–9 and –8 (B)–11 and –10 (C)8 and 9 (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. sqrt(100) = 10. sqrt(121) = 11.Determine Negative Roots: Determine the negative square roots. -sqrt(100) = -10. -sqrt(121) = -11.Place Negative Square Root: Place -sqrt 117 in the correct interval. Since -11 < -sqrt 117 < -10, -sqrt 117 is between -11 and -10.

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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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Math Problems

Grade 8

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 $-10$ .