Question

complete the following statement. use the integers that are closest to the number in the middle.
□ < -√8 < □

Explanation:

Step1: Find the range of $\sqrt{8}$

We know that $2^2 = 4$ and $3^2=9$. Since $4<8 < 9$, taking square roots (and since square root is an increasing function for non - negative numbers), we have $2<\sqrt{8}<3$.

Step2: Find the range of $-\sqrt{8}$

When we multiply an inequality by a negative number, the direction of the inequality sign changes. So, multiplying the inequality $2<\sqrt{8}<3$ by $- 1$, we get $-3<-\sqrt{8}<-2$.

Answer:

$-3 < -\sqrt{8} < -2$