Question

[truong thao my]

rút gon bieu thức

\(\left(3\sqrt{2}+\sqrt{6}\right).\sqrt{6-3\sqrt{3}}\)

\(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)

\(\sqrt{\dfrac{13}{4}+\sqrt{3}}-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)

\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}+\sqrt{\dfrac{129}{16}+\sqrt{2}}\)

\(\sqrt{11+6\sqrt{2}}-\sqrt{\sqrt{8}+3}\)

\(\sqrt{16-6\sqrt{7}}+\sqrt{10-2\sqrt{21}}\)

Answer 1

[huỳnh thị ngọc ngân]

b) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)

= \(\sqrt{3.4-3\sqrt{7}}-\sqrt{3.4+3\sqrt{7}}\)

= \(\sqrt{3.\left(4-\sqrt{7}\right)}-\sqrt{3.\left(4+\sqrt{7}\right)}\)

= \(\sqrt{3}.\sqrt{4-\sqrt{7}}-\sqrt{3}.\sqrt{4+\sqrt{7}}\)

= \(\sqrt{3}.\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\right)\)

\(\)≈ \(-2,449\)

Answer 2

[huỳnh thị ngọc ngân]

\(\sqrt{\dfrac{13}{4}+\sqrt{3}}-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)

= \(\sqrt{\dfrac{13}{4}+\dfrac{4\sqrt{3}}{4}}-\sqrt{\dfrac{7}{4}-\dfrac{4\sqrt{3}}{4}}\)

= \(\sqrt{\dfrac{13+4\sqrt{3}}{4}}-\sqrt{\dfrac{7-4\sqrt{3}}{4}}\)

= \(\dfrac{\sqrt{13+4\sqrt{3}}}{\sqrt{4}}-\dfrac{\sqrt{7-4\sqrt{3}}}{\sqrt{4}}\)

= \(\dfrac{\sqrt{13+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}}{\sqrt{4}}\)

≈ \(2,098\)