Which two integers is –sqrt 123 between? Choices: (A)–11 and –10 (B)–10 and –9 (C)–12 and –11 (D)–14 and –13

Identify Perfect Squares: Identify the perfect squares around 123. The perfect square just below 123 is 121 (11^2). The perfect square just above 123 is 144 (12^2).Calculate Square Roots: Calculate the square roots of 121 and 144. sqrt(121) = 11 sqrt(144) = 12Determine Negative Square Roots: Determine the negative square roots. -sqrt(121) = -11 -sqrt(144) = -12Place Negative Square Roots: Place -sqrt 123 within the correct interval. Since -12 < -sqrt(123) < -11, -sqrt 123 is between -12 and -11.

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Which two integers is $–\sqrt{123}$ between? $\newline$ Choices: $\newline$ (A) $–11$ and $–10$ $\newline$ (B) $–10$ and $–9$ $\newline$ (C) $–12$ and $–11$ $\newline$ (D) $–14$ and $–13$

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Math Problems

Grade 8

Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{123}

between?

\newline

Choices:

\newline

(A)

–11

and

–10

\newline

(B)

–10

and

–9

\newline

(C)

–12

and

–11

\newline

(D)

–14

and

–13

Identify Perfect Squares: Identify the perfect squares around $123$ . The perfect square just below $123$ is $121$ ( $11^2$ ). The perfect square just above $123$ is $144$ ( $12^2$ ).
Calculate Square Roots: Calculate the square roots of $121$ and $144$ . $\sqrt{121} = 11$ $\sqrt{144} = 12$
Determine Negative Square Roots: Determine the negative square roots. $\newline$ $-\sqrt{121} = -11$ $\newline$ $-\sqrt{144} = -12$
Place Negative Square Roots: Place $-\sqrt{123}$ within the correct interval. $\newline$ Since -12 < -\sqrt{123} < -11, $-\sqrt{123}$ is between $-12$ and $-11$ .