Question

Rút gọn các biểu thức :

a) \(\left(2\sqrt{3}+\sqrt{5}\right)\sqrt{3}-\sqrt{60}\)

b) \(\left(5\sqrt{2}+2\sqrt{5}\right)\sqrt{5}-\sqrt{250}\)

c) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)

d) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)

Answer 1

a) \(\left(2\sqrt{3}+\sqrt{5}\right)\sqrt{3}-\sqrt{60}\) = \(6+\sqrt{15}-2\sqrt{15}\)

= \(6-\sqrt{15}\)

b) \(\left(5\sqrt{2}+2\sqrt{5}\right)\sqrt{5}-\sqrt{250}\) = \(5\sqrt{10}+10-5\sqrt{10}\) = \(10\)

c) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\) = \(14-2\sqrt{21}-7+2\sqrt{21}\)

= \(7\)

d) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)

= \(33-3\sqrt{22}-11+3\sqrt{22}\) = \(22\)

Answer 2

a)(2√3+√5)√3-√60
=6+√15-2√15
=6-√15

b)(5√2+2√5)√5-√250
=5√10+10-5√10
=10

c)(√28-√12-√7)√7+2√21
=14-2√21-7+2√21
=7

d)(√99-√18-√11)√11+3√22
=33-3√22-11+3√22
=22