Thu gọn biểu thức sau
\(\left(\sqrt{3}+1\right)\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}\)
Những câu hỏi liên quan
Thu gọn biểu thức sau:
\(\left(\sqrt{3}+1\right)\)\(\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}\)
mình không viết lại đề nha
\(=\sqrt{\frac{\left(\sqrt{3}+1\right)^2.\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)
\(=\sqrt{\frac{\left(3+2\sqrt{3}+1\right).\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)
\(=\sqrt{\frac{\left(4+2\sqrt{3}\right).\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}\)
\(=\sqrt{\frac{56-24\sqrt{3}+28\sqrt{3}-36}{5+\sqrt{3}}}\)
\(=\sqrt{\frac{20+4\sqrt{3}}{5+\sqrt{3}}}\)
\(=\sqrt{\frac{\left(20+4\sqrt{3}\right).\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right).\left(5-\sqrt{3}\right)}}\)
\(=\sqrt{\frac{100-20\sqrt{3}+20\sqrt{3}-12}{5^2-\sqrt{3}^2}}\)
\(=\sqrt{\frac{88}{25-3}}\)
\(=\sqrt{\frac{88}{22}}\)
\(=\sqrt{4}\)
\(=2\)
HỌC TỐT !!!
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Thu gọn biểu thức:
A=\(\left(\sqrt{3}+1\right)\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}\)
\(A=\left(\sqrt{3}+1\right)\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}=\left(\sqrt{3}+1\right)\sqrt{\frac{20+4\sqrt{3}-10\sqrt{3}-6}{5+\sqrt{3}}}=\left(\sqrt{3}+1\right)\sqrt{\frac{4\left(5+\sqrt{3}\right)-2\sqrt{3}\left(5+\sqrt{3}\right)}{5+\sqrt{3}}}=\left(\sqrt{3}+1\right)\sqrt{\frac{\left(4-2\sqrt{3}\right)\left(5+\sqrt{3}\right)}{5+\sqrt{3}}}=\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}=\left(\sqrt{3}+1\right)\sqrt{3-2\sqrt{3}+1}=\left(\sqrt{3}+1\right)\sqrt{\left(\sqrt{3}-1\right)^2}=\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)=3-1=2\Rightarrow A=2\)
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Thu gọn biểu thức:
\(A=\left(\sqrt{3}+1\right)\cdot\left(\frac{14-6\sqrt{3}}{5+\sqrt{3}}\right)\)
\(A=\frac{\left(\sqrt{3}+1\right)\left(14-6\sqrt{3}\right)\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right)}=\frac{4\left(11\sqrt{3}-11\right)}{25^2-\left(\sqrt{3}\right)^2}=\frac{44\left(\sqrt{3}-1\right)}{22}=2\sqrt{3}-2\)
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\(\frac{4\left(11\sqrt{3}-11\right)}{25^2-\left(\sqrt{3}\right)^2}\) Thay Bằng:
\(\frac{4\left(11\sqrt{3}-11\right)}{5^2-\left(\sqrt{3}\right)^2}\)
Cảm ơn bạn!
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tại mình ghi lộn á, 25 chứ k phải 25 bình đâu
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Thu gọn biểu thức sau:
\(B=5\left(\sqrt{2+\sqrt{3}}+\sqrt{3-\sqrt{5}}-\sqrt{\frac{5}{2}}\right)^2-\left(\sqrt{2-\sqrt{3}}+\sqrt{3+\sqrt{5}}-\sqrt{\frac{3}{2}}\right)^2\)
Rút gọn các biểu thức sau:
\(D=\left(\frac{5\sqrt{x-6}}{x-9}-\frac{2}{\sqrt{x}+3}\right):\left(1+\frac{6}{x-9}\right)\)
\(E=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
thu gọn biểu thức\(\sqrt{\left(\sqrt{5}+3\right)^2}+\sqrt{14-6\sqrt{5}}\)
\(\sqrt{\left(\sqrt{5}+3\right)^2}+\sqrt{14-6\sqrt{5}}\)\(=\left|\sqrt{5}+3\right|+\sqrt{9-2.3\sqrt{5}+5}\)
\(=\sqrt{5}+3+\sqrt{\left(3-\sqrt{5}\right)^2}\) \(=\sqrt{5}+3+\left|3-\sqrt{5}\right|\)
\(=\sqrt{5}+3+3-\sqrt{5}=6\) ( do \(3-\sqrt{5}>0\))
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thu gọn biểu thức sau
\(A=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
Câu 3: Rút gọn biểu thức sau:
a. \(\dfrac{1}{\sqrt{5}-1}+\dfrac{1}{1+\sqrt{5}}\)
b. \(\sqrt{14-6\sqrt{5}}+\sqrt{\left(2-\sqrt{5}\right)^2}\)
c. \(\dfrac{2}{\sqrt{5}+\sqrt{3}}-\dfrac{3-\sqrt{15}}{\sqrt{5}-\sqrt{3}}\)
\(a,=\dfrac{\sqrt{5}+1+\sqrt{5}-1}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}=\dfrac{2\sqrt{5}}{4}=\dfrac{\sqrt{5}}{2}\\ b,=\sqrt{\left(3-\sqrt{5}\right)^2}+\left|2-\sqrt{5}\right|=3-\sqrt{5}+\sqrt{5}-2=1\\ c,=\dfrac{2\left(\sqrt{5}-\sqrt{3}\right)}{2}-\dfrac{-\sqrt{3}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{5}-\sqrt{3}}=\sqrt{5}-\sqrt{3}+\sqrt{3}=\sqrt{5}\)
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Rút gọn các biểu thức sau:a) left(sqrt{8}-3sqrt{2}+sqrt{10}right)left(sqrt{2}-3sqrt{0,4}right) b) left(sqrt{28}-2sqrt{14}+sqrt{7}right).sqrt{7}+7sqrt{8}c) 2sqrt{left(sqrt{2}-3right)^2}+sqrt{2left(-3right)^2}-5sqrt{left(-1right)^4} d) left(frac{sqrt{14}-sqrt{7}}{1-sqrt{2}}+frac{sqrt{15}-sqrt{5}}{1-sqrt{3}}right):frac{1}{sqrt{7}-sqrt{5}}
Đọc tiếp
Rút gọn các biểu thức sau:
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\left(\sqrt{2}-3\sqrt{0,4}\right)\) b) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
c) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\) d) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)