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Which two integers is $–\sqrt{39}$ between? $\newline$ Choices: $\newline$ (A) $–7$ and $–6$ $\newline$ (B) $5$ and $6$ $\newline$ (C) $–6$ and $–5$ $\newline$ (D) $6$ and $7$

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Estimate positive and negative square roots

Full solution

Q. Which two integers is

–\sqrt{39}

between?

\newline

Choices:

\newline

(A)

–7

and

–6

\newline

(B)

5

and

6

\newline

(C)

–6

and

–5

\newline

(D)

6

and

7

Identify Perfect Squares: Identify the perfect squares around $39$ . The perfect square just below $39$ is $36$ . The perfect square just above $39$ is $49$ .
Calculate Square Roots: Calculate the square roots of these perfect squares. $\newline$ $\sqrt{36} = 6$ $\newline$ $\sqrt{49} = 7$
Determine Negative Square Roots: Determine the negative square roots. $\newline$ $-\sqrt{36} = -6$ $\newline$ $-\sqrt{49} = -7$
Place Negative Square Roots: Place $-\sqrt{39}$ in relation to $-6$ and $-7$ . Since $-7 < -\sqrt{39} < -6$ , $-\sqrt{39}$ is between $-7$ and $-6$ .

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