Toán Lớp 9: Rút gọn: A = ( √ 6 + √ 20 − 2 √ 3 − √ 5 + √ 15 − 10 √ 2 ) : ( 2 + √ 8 )

Question

Toán Lớp 9:  Rút gọn: A = ( √ 6 + √ 20 − 2 √ 3 − √ 5 + √ 15 − 10 √ 2 ) : ( 2 + √ 8 )

tuanh · Answer

$A =  left( sqrt{6+ sqrt{20}}-2 sqrt{3- sqrt{5}}+ sqrt{15-10 sqrt{2}} right)  :   left(2+ sqrt8 right)$   $ to A =  left( sqrt{ left( sqrt5 right)^2 +2. sqrt{5}.1 + 1^2}- sqrt2. sqrt{ left( sqrt5 right)^2-2. sqrt{5}.1+ 1^2}+ sqrt{ left( sqrt{10} right)^2-2. sqrt{10} sqrt{5} +  left( sqrt5 right)^2} right)  :   left[2 left(1+ sqrt2 right) right]$   $ to A =  left[ sqrt{ left( sqrt5+1 right)^2}- sqrt2. sqrt{ left( sqrt5-1 right)^2}+ sqrt{ left( sqrt{10}- sqrt5 right)^2} right]  :   left[2 left(1+ sqrt2 right) right]$   $ to A =  left[ sqrt5 +1 -  sqrt2 left( sqrt5-1 right) +  left( sqrt{10}- sqrt5 right) right]  :   left[2 left(1+ sqrt2 right) right]$   $ to A =  left(1+ sqrt2 right)  :   left[2 left(1+ sqrt2 right) right]$   $ to A = dfrac12$