Răspuns:
Explicație pas cu pas:
1) a) 3√7-11√7 = √7·(3-11) = -8√7
b) √38:√2 = √(38:2) = √19
c) 3√3·7√7 = 3·7·√(3·7) = 21√21
d) 11·2√21 = 22√21
e) √(-13)² = √13² = 13
f) √(144/121) = √(12²/11²) = 12/11
g) √(25²-15²) = √(625-225) = √400 = 20
h) (4√3+13√3):17 = 17√3:17 = √3
i) 2√3·(8√5-10√5) = 2√3·(-2√5) = -4√(3·5) = -4√15
j) (-2√6/5)² = (2√6/5)² = 4·6/25 = 24/25
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2) a) -13/3√2 = -13√2/(3√2·√2) = -13√2/6
b) 21/√8 = 21/2√2 = 21√2/(2√2·√2) = 21√2/4
c) (√5+3)/√2 = √2(√5+3)/(√2·√2) = (√10+3√2)/2
d) -16/5√2 = -16√2/(5√2·√2) = -16√2/10 = -8√2/5
e) 4/(√17+√13) = 4(√17-√13)/[(√17-√13)(√17+√13)]=
= 4(√17-√13)/(17-13) = √17-√13
f) 27/√3 = 27√3/(√3·√3) = 27√3/3 = 9√3
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3) (3/√2+7/√5)·√10-(7/√6-5/√2)·√12-5√6 =
= [(3√5+7√2)/√10] ·√10 -[(7√2-5√6)/√12]·√12- 5√6 =
= 3√5+7√2-7√2+5√6-5√6 = 3√5
