Which two consecutive integers does −√92 lie between?

Question

Responses
A 8 and 9
B 9 and 10
C −8 and −9
D -9 and -10

Answer 1

To determine the two consecutive integers between which \(-\sqrt{92}\) falls, we first need to calculate \(\sqrt{92}\).

1. Estimate \(\sqrt{92}\):

   • We know that \(9^2 = 81\) and \(10^2 = 100\).
   • Thus, \(9 < \sqrt{92} < 10\).

2. To find \(-\sqrt{92}\):

   • Since \(\sqrt{92}\) is between 9 and 10, we have:
   • \(-10 < -\sqrt{92} < -9\).

This means that \(-\sqrt{92}\) lies between the integers -10 and -9.

Therefore, the answer is D -9 and -10.