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Which two integers is $–\sqrt{55}$ between? $\newline$ Choices: $\newline$ (A) $–8$ and $–7$ $\newline$ (B) $–6$ and $–5$ $\newline$ (C) $–7$ and $–6$ $\newline$ (D) $–10$ and $–9$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{55}

between?

\newline

Choices:

\newline

(A)

–8

and

–7

\newline

(B)

–6

and

–5

\newline

(C)

–7

and

–6

\newline

(D)

–10

and

–9

Identify Perfect Squares: Identify the perfect squares around $55$ . The perfect square just below $55$ is $49$ . The perfect square just above $55$ is $64$ .
Calculate Square Roots: Calculate the square roots of $49$ and $64$ . $\sqrt{49} = 7$ $\sqrt{64} = 8$
Determine Negative Square Roots: Determine the negative square roots. $\newline$ $-\sqrt{49} = -7$ $\newline$ $-\sqrt{64} = -8$
Place Negative Square Roots: Place $-\sqrt{55}$ in relation to $-7$ and $-8$ . Since $-8 < -\sqrt{55} < -7$ , $-\sqrt{55}$ is between $-8$ and $-7$ .

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