Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 610: 14

$-12 \sqrt {13}$

In order to see if a radical is in simplified form, see if any of its factors are perfect squares (meaning that their square root will be an integer). We see that $\sqrt 117$ has factors of 13 and 9. 9 is a perfect square, so we know that we can simplify: $-4\sqrt {117} =-4 \times \sqrt {9} \times \sqrt {13} = -12 \sqrt {13}$