Question

A)√8+√18+√32

B)4√2+√112√18+√28

C)2√2+2√2+√10+4√2+√10

D)√2+√3

E)√27+√12+√27+√12

F)2√3+√27+√75+√48

G)7√32-5√2+√8

Answer 1

Decompomos o radicando em fatores primos:

a) $\sqrt{2*4}+ \sqrt{2*9} + \sqrt{2*16}$
     $2 \sqrt{2} +3 \sqrt{2} +4 \sqrt{2} =9 \sqrt{2~}$

b) $4 \sqrt{2} + \sqrt{7* 2^{4} } + \sqrt{2* 3^{2} } + \sqrt{7* 2^{2} }$
     $4 \sqrt{2} +4 \sqrt{7} +3 \sqrt{2} +2 \sqrt{7} = 7 \sqrt{2} +6 \sqrt{7}$

c) $8 \sqrt{2} +2 \sqrt{10}$

d) $\sqrt{2} + \sqrt{3}$

e) $2 \sqrt{27} +2 \sqrt{12} = 2 \sqrt{ 3^{3} } +2 \sqrt{3* 2^{2} } =2*3 \sqrt{3} +2*2 \sqrt{3}$
   $6 \sqrt{3} +4 \sqrt{3} =10 \sqrt{3}$

f) $2 \sqrt{3} + \sqrt{ 3^{3} } + \sqrt{3* 5^{2} } + \sqrt{3* 2^{4} }$
   $2 \sqrt{3} +3 \sqrt{3} +5 \sqrt{3} +4 \sqrt{3} =14 \sqrt{3}$

g) $7* \sqrt{ 2^{5}} -5 \sqrt{2} + \sqrt{ 2^{3} } = 7* 2^{2} \sqrt{2} -5 \sqrt{2} +2 \sqrt{2} = 25 \sqrt{2}$