Question

complete the following statement. use the integers that are closest to the number in the middle. \square < -\sqrt{117} < \square

Explanation:

Step1: Find nearest perfect squares

$10^2=100$, $11^2=121$

Step2: Relate to $\sqrt{117}$

$10 < \sqrt{117} < 11$

Step3: Negate all terms (reverse inequalities)

$-11 < -\sqrt{117} < -10$

Answer:

$-11 < -\sqrt{17} < -10$
The integers are $\boldsymbol{-11}$ and $\boldsymbol{-10}$