Answer
$34\sqrt{2}$
Work Step by Step
Simplify each radical to obtain
$3\sqrt{9(2)} + 5\sqrt{25(2)}
\\=3\sqrt{3^2(2)}+5\sqrt{5^2(2)}
\\=3\cdot3\sqrt{2}+5\cdot5\sqrt{2}
\\=9\sqrt{2}+25\sqrt{2}.$
RECALL:
The distributive property states that for any real numbers a, b, and c,
$(ac+bc)=(a+b)c.$
Use the rule above to obtain:
$(9+25)\sqrt{2}
\\=34\sqrt{2}.$
