Answer
$2\sqrt{17} - \sqrt{19}$
Work Step by Step
Regroup the terms to obtain:
$=(8\sqrt{17}-6\sqrt{17})+(4\sqrt{19}-5\sqrt{19})$
RECALL:
The distributive property states that for any real numbers a, b, and c:
(1) $ac + bc = (a+b)c$
(2) $ac - bc = (a-b)c$
Use rule (1) above to combine like terms:
$=(8-6)\sqrt{17} + (4-5)\sqrt{19}
\\=2\sqrt{17} + (-1)\sqrt{19}
\\=2\sqrt{17} - \sqrt{19}$
