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+) Ta có: \(2\sqrt{75}-4\sqrt{27}+3\sqrt{12}\)
\(=2\sqrt{25}.\sqrt{3}-4\sqrt{9}.\sqrt{3}+3\sqrt{4}.\sqrt{3}\)
\(=10.\sqrt{3}-12.\sqrt{3}+6.\sqrt{3}\)
\(=4\sqrt{3}\approx6,9282\)
+) Ta có:\(\sqrt{x+6\sqrt{x-9}}\)
\(=\sqrt{x-9+6\sqrt{x-9}+9}\)
\(=\sqrt{\left(\sqrt{x-9}-3\right)^2}\)
\(=\left|\sqrt{x-9}-3\right|\)
\(\frac{2}{\sqrt{5}+\sqrt{3}}+\frac{1}{2-\sqrt{3}}=\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}+\frac{2+\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\)
\(=\frac{2\left(\sqrt{5}-\sqrt{3}\right)}{5-3}+\frac{2+\sqrt{3}}{4-3}=\sqrt{5}-\sqrt{3}+2+\sqrt{3}=\sqrt{5}+2\)
\(=12\sqrt{3}-2\cdot4\sqrt{3}+3\cdot2\sqrt{3}-5\sqrt{3}\)
\(=12\sqrt{3}-8\sqrt{3}+6\sqrt{3}-5\sqrt{3}\)
\(=5\sqrt{3}\)
\(1,2\sqrt{27}+5\sqrt{12}-3\sqrt{48}\\ =2.3\sqrt{3}+5.2\sqrt{3}-3.4\sqrt{3}\\ =6\sqrt{3}+10\sqrt{3}-12\sqrt{3}\\ =4\sqrt{3}\)
\(2,\sqrt{147}+\sqrt{75}-4\sqrt{27}\\ =7\sqrt{3}+5\sqrt{3}-4.3\sqrt{3}\\ =7\sqrt{3}+5\sqrt{3}-12\sqrt{3}\\ =\sqrt{3}\left(7+5-12\right)\\ =0\)
\(3,3\sqrt{2}\left(4-\sqrt{2}\right)+3\left(1-2\sqrt{2}\right)^2\\ =3\sqrt{2}.\left(4-\sqrt{2}\right)+3\left(1-4\sqrt{2}+8\right)\\ =12\sqrt{2}-6+3-12\sqrt{2}+24\\ =21\)
\(4,2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\\ =2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}\\ =\sqrt{5}\left(2-5-4+11\right)\\ =4\sqrt{5}\)
1: =6căn 3+10căn 3-12căn 3=4căn 3
2: =7căn 3+5căn 3-12căn 3=0
3: =12căn 2-6+3(9-4căn 2)
=12căn 2-6+27-12căn 2=21
4: =2căn 5-5căn 5+4căn 5+9 căn 5
=10căn 5
\(2\sqrt{9\left(x-3\right)}-\sqrt{4\left(x-3\right)}=10+\frac{1}{2}\)
\(6\sqrt{\left(x-3\right)}-2\sqrt{\left(x-3\right)}=\frac{21}{2}\)
\(4\sqrt{\left(x-3\right)}=\frac{21}{2}\)
\(\sqrt{\left(x-3\right)}=\frac{21}{8}\)
\(x-3=\frac{441}{64}\)
\(x=\frac{633}{64}\)
a: \(=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)
Ta có: \(A=\sqrt{27}-2\sqrt{12}-\sqrt{75}\)
\(=3\sqrt{3}-2\cdot2\sqrt{3}-5\sqrt{3}\)
\(=-6\sqrt{3}\)
\(\Rightarrow A=3\sqrt{3}-2\cdot2\sqrt{3}-5\sqrt{3}=-4\sqrt{3}\)
a: =2015+6-5=2016
b: =10căn 2+5căn 2-6căn 2=9căn 2
c: =3căn 3-4căn 3-5căn 3=-6căn 3
d: =2căn 3+3căn 3-4căn 3=căn 3
\(A=2015+6-5==2015+1=2016\)
\(B=5\sqrt{2^3}+\sqrt{5^2.2}-2\sqrt{3^2.2}\\ =10\sqrt{2}+5\sqrt{2}-6\sqrt{2}\\ =\left(10+5-6\right)\sqrt{2}=9\sqrt{2}\)
\(C=\sqrt{3^3}-2\sqrt{2^2.3}-\sqrt{5^2.3}\\ =3\sqrt{3}-4\sqrt{3}-5\sqrt{3}\\ =\left(3-4-5\right)\sqrt{3}=-6\sqrt{3}\)
\(D=\sqrt{2^2.3}+\sqrt{3^3}-\sqrt{4^2.3}\\ =2\sqrt{3}+3\sqrt{3}-4\sqrt{3}\\ =\left(2+3-4\right)\sqrt{3}=\sqrt{3}\)
`sqrt{12}-sqrt{75}+sqrt{27}`
`=sqrt{4.3}-sqrt{25.3}+sqrt{9.3}`
`=2sqrt3-5sqrt3+3sqrt3=0`
Ta có : \(\sqrt{12}-\sqrt{75}+\sqrt{27}=2\sqrt{3}-5\sqrt{3}+3\sqrt{3}=0\)