\(A=\frac{5+7\sqrt{5}}{\sqrt{5}}+\frac{11+\sqrt{11}}{1+\sqrt{11}}\)
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\(\frac{5+7\sqrt{5}}{\sqrt{5}}+\frac{11+\sqrt{11}}{1+\sqrt{11}}\)
\(\frac{5+7\sqrt{5}}{\sqrt{5}}+\frac{11+\sqrt{11}}{1+\sqrt{11}}\)
\(=\frac{\sqrt{5}.\left(\sqrt{5}+7\right)}{\sqrt{5}}+\frac{\sqrt{11}.\left(\sqrt{11}+1\right)}{1+\sqrt{11}}\)
\(=\sqrt{5}+7+\sqrt{11}\)
p/s: chúc bạn học tốt
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ohh,mik cung hiểu kha khá r.nhưng bn có thể chỉ lm rõ hơn cho mik đc k?
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a, A = \(\frac{5+7\sqrt{5}}{\sqrt{5}}+\frac{11+\sqrt{11}}{1+\sqrt{11}}\)
b, B = \(\left(1-\sqrt{5}\right).\frac{\sqrt{5}+5}{2\sqrt{5}}\)
c, C = \(1+\left(\frac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\frac{x-\sqrt{x}}{1-\sqrt{x}}\right)\) ( với 0 < bằng x)
Giải giúp ạ- mai mình cần rồi
rút gọn:\(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-4}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
Xem chi tiết
\(\left(1+\frac{11-\sqrt{11}}{1-\sqrt{11}}\right)\left(\frac{11+\sqrt{11}}{1+\sqrt{11}}+1\right)\)
mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)Asqrt{5-sqrt{21}}+sqrt{5+sqrt{21}}
b)Bfrac{sqrt{15}-sqrt{5}}{sqrt{3}-1}+frac{5-2sqrt{5}}{2sqrt{5}-4}
c)Cleft(1+frac{11-sqrt{11}}{1-sqrt{11}}right)left(frac{11+sqrt{11}}{1+sqrt{11}}+1right)
d)Dfrac{sqrt{2}}{sqrt{2}-sqrt{3}}-frac{sqrt{2}}{sqrt{2}+sqrt{3}}
e)Efrac{1}{sqrt{2}-sqrt{3}}sqrt{frac{3sqrt{2}-2sqrt{3}}{3sqrt{2}+2sqrt{3}}}
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mọi người giúp em bài này với,em đang cần gấp ạ
bài 2:rút gọn các biểu thức sau
a)A=\(\sqrt{5-\sqrt{21}}+\sqrt{5+\sqrt{21}}\)
b)B=\(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
c)C=\(\left(1+\frac{11-\sqrt{11}}{1-\sqrt{11}}\right)\left(\frac{11+\sqrt{11}}{1+\sqrt{11}}+1\right)\)
d)D=\(\frac{\sqrt{2}}{\sqrt{2}-\sqrt{3}}-\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}\)
e)E=\(\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
a, \(\sqrt{2}A=\sqrt{10-2\sqrt{3.7}}+\sqrt{10+2\sqrt{3.7}}\)
\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{7}\right)^2}\)
\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{3}+\sqrt{7}=2\sqrt{7}\)
\(\Rightarrow A=\sqrt{14}\)
b, \(B=\frac{\sqrt{5}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}+\frac{\sqrt{5}\left(\sqrt{5}-2\right)}{2\left(\sqrt{5}-2\right)}\)
\(=\sqrt{5}+\frac{\sqrt{5}}{2}=\frac{3\sqrt{5}}{2}\)
c, \(C=\left(1-\sqrt{11}\right)\left(\sqrt{11}+1\right)=1-11=-10\)
d, \(D=\frac{\sqrt{2}\left(\sqrt{2}+\sqrt{3}\right)}{2-3}-\frac{\sqrt{2}\left(\sqrt{2}-\sqrt{3}\right)}{2-3}\)
\(=-2-\sqrt{6}+2-\sqrt{6}=-2\sqrt{6}\)
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Thực hiện phép tính:
a)\(\frac{5}{a-\sqrt{11}}+\frac{1}{3\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
b)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)
c)\(\left(\frac{9-2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2-\left(\frac{9+2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2\)
\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}=\frac{\left(\sqrt{5}-\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}+\frac{\left(\sqrt{5}+\sqrt{3}\right)^2}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\frac{\left(\sqrt{5}+1\right)^2}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}=\frac{8-2\sqrt{15}+8+2\sqrt{15}}{2}-\frac{6+2\sqrt{5}}{4}=\frac{32-6-2\sqrt{5}}{4}=\frac{26-2\sqrt{5}}{4}=\frac{14-\sqrt{5}}{2}\) \(\left(\frac{9-2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2-\left(\frac{9+2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)^2=\left(\frac{9-2\sqrt{14}-9-2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)\left(\frac{9-2\sqrt{14}+9+2\sqrt{14}}{\sqrt{7}-\sqrt{2}}\right)=\frac{-72\sqrt{14}}{\sqrt{7}-\sqrt{2}}\)
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truc can thuc va tinh
a) \(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
b) \(\frac{4}{\sqrt{5}-\sqrt{2}}+\frac{3}{\sqrt{5}-2}-\frac{2}{\sqrt{3}-2}+\frac{\sqrt{3}-1}{6}\)
Bạn xem hộ mk đề cậu b nhé căn 5- căn 2 hay là căn 5 - 2
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\(8\sqrt{\frac{2}{5}}+7\sqrt{\frac{5}{2}}-\frac{\sqrt{33}}{\sqrt{3}}+\frac{10}{\sqrt{11}-1}\)
\(8\sqrt{\frac{2}{5}}+7\sqrt{\frac{5}{2}}-\frac{\sqrt{33}}{\sqrt{3}}+\frac{10}{\sqrt{11}-1}\\ =8\sqrt{\frac{10}{5^2}}+7\sqrt{\frac{10}{2^2}}-\sqrt{11}+\frac{10\left(\sqrt{11}+1\right)}{\left(\sqrt{11}-1\right)\left(\sqrt{11}+1\right)}\\ =\frac{8\sqrt{10}}{5}+\frac{7\sqrt{10}}{2}-\sqrt{11}+\frac{10\left(\sqrt{11}+1\right)}{10}\\ =\frac{16\sqrt{10}+35\sqrt{10}}{10}-\sqrt{11}+\sqrt{11}+1\\ =\frac{51\sqrt{10}}{10}+1\\ =\frac{10+51\sqrt{10}}{10}\)
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Tính A= \(\frac{1+\sqrt{11}}{2+\sqrt{11}}+\sqrt{\frac{2}{18-5\sqrt{11}}}\)
Tính
A/left(frac{2sqrt{3}-sqrt{6}}{sqrt{8}-2}-frac{sqrt{216}}{3}right).frac{1}{sqrt{6}}
B/ left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}
C/ frac{5}{4-sqrt{11}}+frac{1}{3+sqrt{7}}-frac{6}{sqrt{7}-2}-frac{sqrt{7}-5}{2}
D/ frac{sqrt{5}-sqrt{3}}{sqrt{5}+sqrt{3}}+frac{sqrt{5}+sqrt{3}}{sqrt{5}-sqrt{3}}-frac{sqrt{5}+1}{sqrt{5}-1}
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Tính
A/\(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right).\frac{1}{\sqrt{6}}\)
B/ \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
C/ \(\frac{5}{4-\sqrt{11}}+\frac{1}{3+\sqrt{7}}-\frac{6}{\sqrt{7}-2}-\frac{\sqrt{7}-5}{2}\)
D/ \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)