(4+√15).(√10-√6).√(4-√15)
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15 tháng 12 2022
1: \(=-145\cdot13+145\cdot57+57\cdot10-57\cdot145=-1315\)
2: \(=17\cdot15-17\cdot16+16\cdot17-16\cdot20=255-320=-65\)
3: \(=-38\cdot25+38\cdot4-25\cdot4+25\cdot38=13\cdot4=52\)
4: \(=23\cdot145-23\cdot17-145\cdot23+145\cdot6=479\)
5: \(=24\cdot15-24\cdot4+4\cdot24-4\cdot15=360-60=300\)
6: \(=199\left(15-17+17-5\right)=199\cdot10=1990\)
7: \(=-39\cdot5+39\cdot99+99\cdot10-99\cdot39=795\)
MG
1
H9
HT.Phong (9A5)
CTVHS
20 tháng 6 2023
\(\left(\sqrt{\text{1}0}-\sqrt{6}\right)\cdot\left(4+\sqrt{15}\right)\cdot\sqrt{4-\sqrt{15}}\)
\(=\left(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{10}+\sqrt{6}\right)^2\left(4-\sqrt{15}\right)}\)
\(=\sqrt{\left(10+6+2\sqrt{60}\right)\left(4-\sqrt{15}\right)}\)
\(=\sqrt{\left(16+4\sqrt{15}\right)\left(4-\sqrt{15}\right)}\)
\(=\sqrt{64-16\sqrt{15}+16\sqrt{15}-60}\)
\(=\sqrt{4}=2\)
BT
2
18 tháng 5 2018
ta có : (ghi lại đề)
=6+12+18+24+30/3+6+9+12+15
=2*(3/3+6/6+9/9+12/12+15/15)
=2*(1+1+1+1+1)
=2*5=10
chúc main học tốt nhé
26 tháng 6 2021
`1)A=sqrt{4+sqrt{10+2sqrt5}}+sqrt{4-sqrt{10+2sqrt5}}`
`<=>A^2=4+sqrt{10+2sqrt5}+4-sqrt{10+2sqrt5}+2sqrt{16-10-2sqrt5}`
`<=>A^2=8+2sqrt{6-2sqrt5}`
`<=>A^2=8+2sqrt{(sqrt5-1)^2}`
`<=>A^2=8+2(sqrt5-1)`
`<=>A^2=6+2sqrt5=(sqrt5+1)^2`
`<=>A=sqrt5+1(do \ A>0)`
`b)B=sqrt{35+12sqrt6}-sqrt{35-12sqrt6}`
Vì `35+12sqrt6>35-12sqrt6`
`=>B>0`
`B^2=35+12sqrt6+35-12sqrt6-2sqrt{35^2-(12sqrt6)^2}`
`<=>B^2=70-2sqrt{361}`
`<=>B^2=70-2sqrt{19^2}=70-38=32`
`<=>B=sqrt{32}=4sqrt2(do \ B>0)`
`3)(4+sqrt{15})(sqrt{10}-sqrt6)sqrt{4-sqrt{15}}`
`=sqrt{4+sqrt{15}}.sqrt{4-sqrt{15}}.sqrt{4+sqrt{15}}(sqrt{10}-sqrt6)`
`=sqrt{16-15}.sqrt2(sqrt5-sqrt3).sqrt{4+sqrt{15}}`
`=sqrt{8+2sqrt{15}}(sqrt5-sqrt3)`
`=sqrt{5+2sqrt{5.3}+3}(sqrt5-sqrt3)`
`=sqrt{(sqrt5+sqrt3)^2}(sqrt5-sqrt3)`
`=(sqrt5+sqrt3)(sqrt5-sqrt3)`
`=5-3=2`
29 tháng 8 2021
2: \(\dfrac{\sqrt{108}}{\sqrt{3}}=6\)
13: \(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
\(=\sqrt{5}-\sqrt{3}-2\sqrt{5}+\sqrt{3}\)
\(=-\sqrt{5}\)
14: \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
=2
HP
29 tháng 8 2021
12.
\(\dfrac{\sqrt{108}}{\sqrt{3}}=\dfrac{\sqrt{36}.\sqrt{3}}{\sqrt{3}}=\sqrt{36}=6\)
13.
\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}-\sqrt{\left(2\sqrt{5}-\sqrt{3}\right)^2}\)
\(=\left|\sqrt{3}-\sqrt{5}\right|-\left|2\sqrt{5}-\sqrt{3}\right|\)
\(=\sqrt{5}-\sqrt{3}-2\sqrt{5}+\sqrt{3}\)
\(=-\sqrt{5}\)
\(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
=32-30
=2