Toán Lớp 9: Giúp em với ạ . Rút gọn :
a) √(5-2) + √(5-3)
b) √7-2 √10 – √6-2 √5
c ) { √99}{ √11} + { √28}{7} – √81
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Toán Lớp 9: Giúp em với ạ . Rút gọn :
a) √(5-2) + √(5-3)
b) √7-2 √10 – √6-2 √5
c ) { √99}{ √11} + { √28}{7} – √81
Comments ( 2 )
a,
$=\sqrt{3}+\sqrt{2}$
b,
$=\sqrt{(\sqrt{5}-\sqrt{2})^2}-\sqrt{(\sqrt{5}-1)^2}$
$=|\sqrt{5}-\sqrt{2}|-|\sqrt{5}-1|$
$=\sqrt{5}-\sqrt{2}-\sqrt{5}+1$
$=1-\sqrt{2}$
$=3+\dfrac{2\sqrt{7}}{7}-9$
$=\dfrac{2\sqrt{7}}{7}-6$
$=\dfrac{2\sqrt{7}-42}{7}$
=sqrt3 + sqrt2
b) sqrt{7-2sqrt10}-sqrt{6-2sqrt5}
=sqrt{5-2sqrt10+2}-sqrt{5-2sqrt5+1}
=sqrt{(sqrt5)^2-2*sqrt5*sqrt2+(sqrt2)^2}-sqrt{(sqrt5)^2-2*sqrt5*1+1^2}
=sqrt{(sqrt5-sqrt2)^2}-sqrt{(sqrt5-1)^2}
=|sqrt5-sqrt2|-|sqrt5-1|
=sqrt5-sqrt2-sqrt5+1 (Vì sqrt5-sqrt2>0 ; sqrt5-1>0 )
=-sqrt2+1
c) sqrt99/sqrt11 +sqrt28/7 -sqrt81
=sqrt{99/11}+(2sqrt7)/7-9
=sqrt9 + (2sqrt7)/7-9
=3+(2sqrt7)/7-9
=(2sqrt7)/7 -6
=(2sqrt7)/7 – 42/7
=(2sqrt7-42)/7