Tính \(\sqrt{5+2\sqrt{6}}\)
K
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HT
1
6 tháng 11 2021
\(=\sqrt{\dfrac{\left(5-2\sqrt{6}\right)^2}{25-24}+\sqrt{\left(3-\sqrt{6}\right)^2}}=\sqrt{25+24-20\sqrt{6}+3-\sqrt{6}}=\sqrt{52-21\sqrt{6}}\)
25 tháng 6 2021
a) Ta có: \(A=\sqrt{\sqrt{3}+\sqrt{2}}\cdot\sqrt{\sqrt{3}-\sqrt{2}}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}\)
\(=\sqrt{3-2}=1\)
b) Ta có: \(B=\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}\)
\(=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}\)
\(=2\sqrt{3}\)
25 tháng 6 2021
`A=sqrt{sqrt3+sqrt2}.sqrt{sqrt3-sqrt2}`
`=sqrt{(sqrt3+sqrt2)(sqrt3-sqrt2)}`
`=sqrt{3-2}=1`
`b)B=sqrt{5-2sqrt6}+sqrt{5+2sqrt6}`
`=sqrt{3-2sqrt6+2}+sqrt{3+2sqrt6+2}`
`=sqrt{(sqrt3-sqrt2)^2}+sqrt{(sqrt3+sqrt2)^2}`
`=sqrt3-sqrt2+sqrt3+sqrt2=2sqrt3`
`c)C=3-sqrt{3-sqrt5}`
`=3-sqrt{(6-2sqrt5)/2}`
`=3-sqrt{(sqrt5-1)^2/2}`
`=3-(sqrt5-1)/sqrt2`
`=3-(sqrt{10}-sqrt2)/2`
`=(6-sqrt{10}+sqrt2)/2`
17 tháng 10 2023
a) \(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}-\dfrac{6}{\sqrt{6}}=\dfrac{3}{2}\sqrt{6}+\dfrac{2}{3}\sqrt{6}-2\sqrt{6}-\dfrac{6}{\sqrt{6}}\)
\(=\dfrac{1}{6\sqrt{6}}-\dfrac{6}{\sqrt{6}}=-\dfrac{35}{6\sqrt{6}}\)
b)\(\left(\sqrt{6}+\sqrt{5}\right)^2+\left(\sqrt{6}-\sqrt{5}\right)^2\)
\(=6+2\sqrt{30}+5+6-2\sqrt{30}+5=22\)
T
28 tháng 8 2023
\(\dfrac{2\left(\sqrt{6-2\sqrt{5}}+6-2\sqrt{5}+1\right)}{\sqrt{6-2\sqrt{5}}}\)
\(=\dfrac{2\left[\left(\sqrt{\sqrt{5^2}-2\sqrt{5}+1}\right)+6-2\sqrt{5}+1\right]}{\sqrt{5^2-2\sqrt{5}+1}}\)
\(=\dfrac{2\left[\sqrt{\left(\sqrt{5}-1\right)^2}+6-2\sqrt{5}+1\right]}{\sqrt{\left(\sqrt{5}-1\right)^2}}\)
\(=\dfrac{2\left(\left|\sqrt{5}-1\right|+6-2\sqrt{5}+1\right)}{\left|\sqrt{5}-1\right|}\)
\(=\dfrac{2\left(\sqrt{5}-1+6-2\sqrt{5}+1\right)}{\sqrt{5}-1}\)
\(=\dfrac{2\left(-\sqrt{5}+6\right)}{\sqrt{5}-1}\)
#Ayumu
25 tháng 9 2021
1) \(=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)
2) \(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}=\sqrt{3}+\sqrt{2}\)
3) \(=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\sqrt{5}-\sqrt{2}\)
5) \(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)
6) \(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\sqrt{7}-\sqrt{3}\)
7) \(=\sqrt{\left(3+\sqrt{2}\right)^2}=3+\sqrt{2}\)
RK
22 tháng 6 2021
a) A= \(\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)
Vì \(\left\{{}\begin{matrix}2=\sqrt{4}< \sqrt{5}\\2\sqrt{2}=\sqrt{8}>\sqrt{5}\end{matrix}\right.\) nên A = \(\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)
= \(\sqrt{5}-2+2\sqrt{2}-\sqrt{5}\)
= \(2\left(\sqrt{2}-1\right)\)
RK
22 tháng 6 2021
b) B = \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\) (B > 0)
Ta có:
B2 = \(6+2\sqrt{5}-2\sqrt{\left(6+2\sqrt{5}\right)\left(6-2\sqrt{5}\right)}+6-2\sqrt{5}\)
= \(12-2\sqrt{36-20}\)
= \(12-8\)
= \(4\)
\(\Rightarrow\) B =\(\pm2\) nhưng vì B > 0 nên B = 2
Vậy B = 2
25 tháng 9 2021
a)A=\(2\sqrt{3}-8\sqrt{3}+7\sqrt{3}=\sqrt{3}\)
b)B\(=\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{\left(2-\sqrt{5}\right)^2}=3-\sqrt{5}+\sqrt{5}-2=1\)
d)\(=\dfrac{\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)}{1}+1-\sqrt{5}-\dfrac{11\left(2\sqrt{5}-3\right)}{11}=5\sqrt{5}+5-10-2\sqrt{5}+1-\sqrt{5}-2\sqrt{5}+3=-1\)
9 tháng 10 2021
5: Ta có: \(\dfrac{2-\sqrt{2}}{1-\sqrt{2}}+\dfrac{\sqrt{2}-\sqrt{6}}{\sqrt{3}-1}\)
\(=-\sqrt{2}-\sqrt{2}\)
\(=-2\sqrt{2}\)
AH
Akai Haruma
Giáo viên
26 tháng 8 2023
Lời giải:
a.
\(=\sqrt{5+2.2\sqrt{5}+2^2}-\sqrt{5-2.2\sqrt{5}+2^2}\)
$=\sqrt{(\sqrt{5}+2)^2}-\sqrt{(\sqrt{5}-2)^2}$
$=|\sqrt{5}+2|-|\sqrt{5}-2|=(\sqrt{5}+2)-(\sqrt{5}-2)=4$
b.
$=\sqrt{3-2.3\sqrt{3}+3^2}+\sqrt{3+2.3.\sqrt{3}+3^2}$
$=\sqrt{(\sqrt{3}-3)^2}+\sqrt{(\sqrt{3}+3)^2}$
$=|\sqrt{3}-3|+|\sqrt{3}+3|$
$=(3-\sqrt{3})+(\sqrt{3}+3)=6$
c.
$=\sqrt{2+2.3\sqrt{2}+3^2}-\sqrt{2-2.3\sqrt{2}+3^2}$
$=\sqrt{(\sqrt{2}+3)^2}-\sqrt{(\sqrt{2}-3)^2}$
$=|\sqrt{2}+3|-|\sqrt{2}-3|$
$=(\sqrt{2}+3)-(3-\sqrt{2})=2\sqrt{2}$
\(\sqrt{5+2\sqrt{6}}=\sqrt{2+2.\sqrt{2}.\sqrt{3}+3}=\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}=\sqrt{2}+\sqrt{3}\)