Đáp án+Giải thích các bước giải:
`a,(\sqrt{5}+\sqrt{6})^2`
`=5+6+2\sqrt{5.6}`
`=11+2\sqrt{5.6}`
`(\sqrt{21})^2`
`=21`
`5.6>5.5`
`=>\sqrt{5.6}>5`
`=>2\sqrt{5.6}>10`
`=>11+2\sqrt{5.6}>10+11=21`
`=>\sqrt{5}+\sqrt{6}>\sqrt{21}`
`c,(\sqrt{11}+\sqrt{15})^2`
`=11+15+2\sqrt{11.15}`
`=26+2\sqrt{165}`
`(\sqrt{12}+\sqrt{14})^2`
`=12+14+2\sqrt{12.14}`
`=26+2\sqrt{168}`
`2\sqrt{168}>2\sqrt{165}`
`=>26+2\sqrt{168}>26+2\sqrt{165}`
`=>(\sqrt{12}+\sqrt{14})^2>(\sqrt{11}+\sqrt{15})^2`
`=>\sqrt{12}+\sqrt{14}>\sqrt{11}+\sqrt{15}`
`c,17^14>16^14`
`=>17^14>2^56>2^55`
`=>17^14>32^11`
`=>17^14>30^11`
`d,B=1+2+3+......+1000000`
Từ 1 đến 1000000 có 1000000 số
`=>B=(1000001.1000000)/2`
`=>B=1000001.500000`
`A=1.2.3.4......20`
`=(1.2.3.4.5).(6.7.8.9.10).(11.12.13.14.15).(16.17.18.19.20)`
`=120.30240.360360.1860480`
`=(120.360360).1860480.30240`
`=43243200.1860480.30240`
Ta thấy:
`1000001<43243200`
`500000<1860480`
`=>1000001.500000<43243200.1860480`
Mà `43243200.1860480<43243200.1860480.30240`
`=>A>B`
