Question

calculati:a) 12/radical din 2 - 14/radical din 8+ 16 /radical din 32 -18/3 radical din 2 b) 6/radical din 5 - 6/radical 20 +6/radical din 45 - 6/5 radical5 . C) 21/10radical6 -28/radical 24 + 24/radical 150 - 36/3radical 6 . D)9/radical 18 - 9/radical 8 +9/6 radical 2 -9/6 radical 8 2. rationalizari numitorii: a)4/radical din5 -1.b)6/3+ radical din 6.c) 15/radical7 +radical2. d) 6/3radical2- 2 radical3

Answer 1

·a) 12/√2 - 14/√8+ 16 /√32-18/3√2=12√2/2-14/2√2+16/4√2-18√2/6=
6√2-14√2/4+16√2/8-3√2=
6√2-3√2-7√2/2+2√2=
5√2-7√2/2=
(10√2-7√2)/2=3√2/2

b) 6/√5 - 6/√20 +6/√45 - 6/5√5=6√5/5-6/2√5+6/3√5-6√5/25=
6√5/5-6√5/10+6√5/15-6√5/25=
6√5(1/5-1/10+1/15-1/25)=
6√5(30-15+10-6)/150=
(6√5·19)/150=(2√5·19)/50=19√5/25


C) 21/10√6 -28/√24 + 24/√150 - 36/3√ 6 =
21√6/60-28/2√6+24/5√6-36√6/18=
21√6/60-28√6/12+24√6/30-36√6/18=
(21√6·3-28√6·15+24√6·6-36√6·10)/180=
(63√6-420√6+144√6-360√6)/180=573√6/180=191√6/60


D)9√18 - 9/√ 8 +9/6√ 2 -9/6√8=
9/3√2-9/2√2+9√2/12-9/12√2=
9√2/6-9√2/4+9√2/12-9√2/12=
9√2/6-9√2/4=
9√2(1/6-1/4)=
9√2(2/12-3/12)=-9√2/12
 
2.a)4/(√5 -1)=4(√5+1)/(√5-1)(√5+1)=4(√5-1)/(5-1)=4(√5-1)/4=√5-1

b)6/(3+ √6)=6(3-√6)/(9-6)=6(3-√6)/3=(18-6√6)/3=3(6-2√6)/3=6-2√6

c) 15/(√7 +√2)=15(√7-√2)/(7-2)=15(√7-√2)/5=3(√7-√2)

 d) 6/(3√2- 2√3)=6(3√2+2√3)/(18-12)=6(3√2+2√3)/6=3√2+2√3