Tính :
a) √9−4√5−√14+6√5;
b) (3√2+√10)√28−12√5;
c) √13−√160−√53+4√60;
d) √2+√3(√6−√2).
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+) Sử dụng công thức: √A2B=|A|√B={AkhiA≥0−AkhiA<0.
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a)√9−4√5−√14+6√5=√(√5)2−2.2√5+22−√32+2.3.√5+(√5)2=√(√5−2)2−√(3+√5)2=|√5−2|−|3+√5|=√5−2−3−√5=−5. c)√13−√160−√53+4√60=√13−√42.10−√53+4.√22.15=√13−4√10−√53+8√15=√(2√2)2−2.2√2.√5+(√5)2−√(4√3)2+2.4√3.√5+(√5)2=√(2√2−√5)2−√(4√3+√5)2=|2√2−√5|−|4√3+√5|=2√2−√5−4√3−√5=2√2−2√5−4√3. |
b)(3√2+√10)√28−12√5=√2(3+√5)√28−12√5=(3+√5)√56−24√5=(3+√5)√62−2.6.2√5+(2√5)2=(3+√5)√(6−2√5)2=(3+√5)|6−2√5|=(3+√5).2(3−√5)=2(32−5)=8. d)√2+√3(√6−√2)=√2+√3.√2(√3−1)=√4+2√3(√3−1)=√3+2√3+1(√3−1)=√(√3+1)2.(√3−1)=|√3+1|(√3−1)=(√3+1)(√3−1)=3−2=1. |