Question

Calculati:
A)radical din 18-radical din 8-radical din 2+radical din 50
B)2radical din 5+7radical din 5+radical din 180-17 radical din 5
C)2 radical din 500-3 radical din 125+7 radical din 45-5 radical 5
Rezolvare pas cu pas va rog!!

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

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