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Which two integers is $–\sqrt{38}$ between? $\newline$ Choices: $\newline$ (A) $–5$ and $–4$ $\newline$ (B) $–7$ and $–6$ $\newline$ (C) $4$ 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{38}

between?

\newline

Choices:

\newline

(A)

–5

and

–4

\newline

(B)

–7

and

–6

\newline

(C)

4

and

5

\newline

(D)

6

and

7

Calculate Perfect Squares: Calculate the perfect squares just below and just above $38$ . The perfect square just below $38$ is $36$ , and the perfect square just above $38$ is $49$ .
Compute Square Roots: Compute the square roots of $36$ and $49$ . $\sqrt{36} = 6$ and $\sqrt{49} = 7$ .
Determine Negative Square Roots: Determine the negative square roots: $-\sqrt{36} = -6$ and $-\sqrt{49} = -7$ .
Place Negative Square Roots: Place $-\sqrt{38}$ relative to $-6$ and $-7$ . Since $38$ is between $36$ and $49$ , $-\sqrt{38}$ is between $-7$ and $-6$ .

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