Question

Calculati: a)√12 + √27 ; b)3√18 + 4√32 ; c) 2 √20 - √45 ; d) 4√28-5√44+2√99-√700 ; e) 2√12-5√27 + 0,2√300 ; f) -5√2 + 0, (3)√18-0,25√32. Va rog, am nevoie!

Answer 1

a)√12 + √27
(1) 12=2^2*3=>√12=2√3
(2) 27=3^3=>27=3^2*3=>√27=3√3
Din (1) si (2)=>√12 + √27=2√3+3√3=>√12 + √27=5√3
b)3√18 + 4√32
(1) 18=2*3^2=>√18=3√2
(2) 32=2^5=>4*32=2^4*2=>√32=2^2√2=>√32=4√2
Din (1) si (2)=>3√18 + 4√32=3*3√2+4*4√2=>3√18 + 4√32=9√2+16√2=>
=>3√18 + 4√32=25√2
 c) 2 √20 - √45
(1) 20=2^2*5=>√20=2√5
(2) 45=3^2*5=>√45=3√5
Din (1) si (2)=>2 √20 - √45=2*2√5-3√5=>2 √20 - √45=4√5-3√5=>
=>2 √20 - √45=√5
d) 4√28-5√44+2√99-√700
(1) 28=2^2*7=>√28=2√7
(2) 44=2^2*11=>√44=2√11
(3) 99=3^2*11=>√99=3√11
(4) 700=10^2*7=>√700=10√7
Din (1),(2),(3) si (4)=>4√28-5√44+2√99-√700=4*2√7-5*2√11+2*3√11-10√7=>
=>4√28-5√44+2√99-√700=8√7-10√11+6√11-10√7=>
=>4√28-5√44+2√99-√700=8√7-10√7-10√11+6√11=>
=>4√28-5√44+2√99-√700=-2√7-4√11=>
=>4√28-5√44+2√99-√700=-2(√7+2√11)
e) 2√12-5√27 + 0,2√300
(1) 12=2^2*3=>√12=2√3
(2) 27=3^3=>27=3^2*3=>√27=3√3
(3) 300=10^2*3=>√300=10√3
Din (1),(2), si (3) =>2√12-5√27 + 0,2√300=2*2√3-5*3√3+0,2*10√3=>
=>2√12-5√27 + 0,2√300=4√3-15√3+2√3=>
=>2√12-5√27 + 0,2√300= -9√3
f) -5√2 + 0, (3)√18-0,25√32
(1) 0, (3)=3/9=>0, (3)=1/3
(2) 18=2*3^2=>√18=3√2
(3) 32=2^5=>4*32=2^4*2=>√32=2^2√2=>√32=4√2
Din (1),(2), si (3) =>-5√2 + 0, (3)√18-0,25√32=-5√2 +1/3*3√2-0,25*4√2=>
=>-5√2 + 0, (3)√18-0,25√32=-5√2 +√2-√2=>
=>-5√2 + 0, (3)√18-0,25√32=-5√2