Question

complete the following statement. use the integers that are closest to the number in the middle. \\(\square < -\sqrt{141} < \square\\)

Explanation:

Step1: Find perfect squares around 141

We know that $12^2 = 144$ and $11^2=121$. So, $11^2=121<141 < 12^2 = 144$.

Step2: Take square roots and apply negative sign

Taking square roots (since square root is an increasing function for non - negative numbers), we get $\sqrt{121}<\sqrt{141}<\sqrt{144}$, which simplifies to $11 < \sqrt{141}<12$. Now, multiplying each part of the inequality by - 1 (and reversing the inequality signs because we are multiplying by a negative number), we have $- 12<-\sqrt{141}<-11$.

Answer:

-12, -11 (in the order of the left and right boxes respectively, so the left box is -12 and the right box is -11)