Đáp án+Giải thích các bước giải:
`a)`
`2 ; \sqrt{3}`
`2 = \sqrt{4}`
` 4 > 3 -> \sqrt{4} > \sqrt{3}`
`-> 2 > \sqrt{3}`
---------------------------------
`8 ; \sqrt{63}`
` 8 = \sqrt{64}`
`64 > 63 -> \sqrt{64} > \sqrt{63}`
`-> 8 > \sqrt{63}`
------------------------------------
`6 ; \sqrt{39}`
` 6 = \sqrt{36}`
`36 < 39 -> \sqrt{36} < \sqrt{39}`
`-> 6 < \sqrt{39}`
-----------------------------------
`5 ; \sqrt{24}`
` 5 = \sqrt{25}`
` 25 > 24 -> \sqrt{25} > \sqrt{24}`
`-> 5 > \sqrt{24}`
-----------------------------------
`-\sqrt{5} ; -2`
`-2 = -\sqrt{4}`
`-5 < -4 -> -\sqrt{5} < -\sqrt{4}`
`-> -\sqrt{5} < -2`
`b)`
`6 ; \sqrt{5} + \sqrt{26}`
`6 = 5 + 1 = \sqrt{25} + \sqrt{1}`
`\sqrt{25} < \sqrt{26} ; \sqrt{5} > \sqrt{1}`
`-> \sqrt{5} + \sqrt{26} > 6`
-----------------------------------------------
`7 ; \sqrt{7} + \sqrt{15}`
`7 = 4 + 3 = \sqrt{16} + \sqrt{9}`
` \sqrt{16} > \sqrt{15} ; \sqrt{9} > \sqrt{7}`
`-> 7 > \sqrt{7} + \sqrt{15}`
----------------------------------------------
`7;\sqrt{26} + \sqrt{5}`
`7 = 5 + 2 = \sqrt{25} + \sqrt{4}`
`\sqrt{25} < \sqrt{26} ; \sqrt{4} < \sqrt{5}`
`-> 7 < \sqrt{26} + \sqrt{5}`
----------------------------------------------
`\sqrt{65} ; \sqrt{8} + \sqrt{24}`
`\sqrt{65} > \sqrt{8} + \sqrt{24}`
---------------------------------------------
`\sqrt{25-16} ; \sqrt{25} - \sqrt{16}`
`\sqrt{25-16} = \sqrt{9} = 3`
`\sqrt{25} - \sqrt{16} = 5 - 4 = 1`
`3 > 1 -> \sqrt{25-16} > \sqrt{25} - \sqrt{16}`
`c)`
`4 ; 2\sqrt{3}`
` 4 = \sqrt{16}`
`2\sqrt{3} = \sqrt{4} . \sqrt{3} = \sqrt{12}`
`16 > 12 -> \sqrt{16} > \sqrt{12}`
`-> 4 > 2\sqrt{3}`
---------------------------------------------
`8 ; \sqrt{5}\sqrt{20}`
`8 = \sqrt{64}`
`\sqrt{5}\sqrt{20} = \sqrt{100}`
`64 < 100 -> \sqrt{64} < \sqrt{100}`
`-> 8 < \sqrt{5}\sqrt{20}`
---------------------------------------------
`18 ; \sqrt{15}\sqrt{17}`
`18 = \sqrt{324}`
`\sqrt{15}\sqrt{17} = \sqrt{255}`
`324 > 255 -> \sqrt{234} > \sqrt{255}`
`-> 18 > \sqrt{15}\sqrt{17}`
--------------------------------------------
`-30 ; -5\sqrt{35}`
`-30 = -\sqrt{900}`
`-5\sqrt{35} = -\sqrt{25}\sqrt{35} = -\sqrt{875}`
` -900 < -875 -> -\sqrt{900} < -\sqrt{875}`
`-> -30 < -5\sqrt{35}`
-------------------------------------------------------
`-12 ; \sqrt{8}\sqrt{15}`
`-12 = -\sqrt{144}`
`\sqrt{8}\sqrt{15} = \sqrt{120}`
`-144 < 120 -> -\sqrt{144} < \sqrt{120}`
`-> -12 < \sqrt{8}\sqrt{15}`
