Question

Calculati. Cine face cel mai corect ii dau coroana
Va rog

Answer 1

Sper ca se observa rezolvarea ......

Answer 2

a)
2/√12 + 5/√75 - ( 3√3/8 + 6 / √108 ) =
= 2/2√3 + 5/5√3 - ( 3√3/8 + 6/6√3)= → simplific pe 2 cu 2, pe 5 cu 5, 6 cu 6
= √3/3  + √3/3 - ( 3√3/8 + √3/3) = →rationalizez numitorii
= 2√3/3 - ( 9√3/24 + 8√3/24)→cmmmc (8 si 3)=24,amplific cu 3,respectiv cu 8
= 2√3/3 - 17√3/24 =→ amplific prima fractie cu 8
= 16√3 / 24  - 17 √3/ 24 = 
= - √ 3 /24

b) 6 √2 /√3 + 3 /2√3  + 6√3/3√2 + 4√3/2√2 = → rationalizam numitorii
= 6√6 / 3 + 3√6/12 + 6√6 /6 +  4√6/4= → simplificam
= 2√6 + √6/4 + √6 + √6=
= 4√6 + √6/4 =
= 16√6/4 + √6 /4 =
= 17√6/4

c)
3√2/4√3 - 5/√6 + 2√3/3√2 - ( √24 + 12/2√6) =
= 3√6/12 - 5√6/6 + 2√6/6 - ( 2√6 + 6√6/6)=
= 3√6 /12 - 10√6/12 + 4√6/12 - ( 2√6 + √6) =
= - 3√6/12 - 3√6=
= - 3√6/12 - 36√6/12=
= - 39√6 /12 = 
= - 13√6/4

d)   2√5/ 5√2 - 20/√10 + ( 2√10 / 15 - 30/ √40)=
= 2√10 /10 - 20 √10/10  + ( 2√10/15 - 30√10/20)=
= - 18√10/10 + ( 4√10/30 - 45√10/30)=
= - 18 √10 /10 - 41√10/30=
= - 54√10/30 - 41 √10 /30=
= - 95√10/30 = 
= - 19√10/6