Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Exercise Set 5.4 - Page 299: 105

between $-7$ and $-6$

$47$ is betwen the perfect squares $36$ and $49$. This means that : $\sqrt{36}\lt \sqrt{47} \lt \sqrt{49}\\ 6 \lt \sqrt{47} \lt 7$ Note that $1\lt 2\lt3$, but $-3 \lt -2 \lt -1$ Since $6 \lt \sqrt{47} \lt 7$, then $-7 \lt -\sqrt{47} \lt -6$. Therefore, $-\sqrt{47}$ is between the integers $-7$ and $-6$.