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Which two integers is $–\sqrt{69}$ between? $\newline$ Choices: $\newline$ (A) $–9$ and $–8$ $\newline$ (B) $–7$ and $–6$ $\newline$ (C) $–10$ and $–9$ $\newline$ (D) $–6$ and $–5$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{69}

between?

\newline

Choices:

\newline

(A)

–9

and

–8

\newline

(B)

–7

and

–6

\newline

(C)

–10

and

–9

\newline

(D)

–6

and

–5

Identify Perfect Squares: Identify the perfect squares closest to $69$ . The perfect square just below $69$ is $64$ . The perfect square just above $69$ is $81$ .
Calculate Square Roots: Calculate the square roots of these perfect squares. $\newline$ $\sqrt{64} = 8$ $\newline$ $\sqrt{81} = 9$
Determine Negative Square Roots: Determine the negative square roots. $\newline$ $-\sqrt{64} = -8$ $\newline$ $-\sqrt{81} = -9$
Place Negative Square Roots: Place $-\sqrt{69}$ in relation to $-8$ and $-9$ . Since $-9 < -\sqrt{69} < -8$ , $-\sqrt{69}$ is between $-9$ and $-8$ .

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