60/57 + 11/38=?
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mình làm vài câu cho bạn tham khảo,các câu còn lại thì bạn làm tương tự thôi
23.\(\sqrt{14-2\sqrt{33}}=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\left|\sqrt{11}-\sqrt{3}\right|=\sqrt{11}-\sqrt{3}\)
28. \(\sqrt{25-4\sqrt{6}}=\sqrt{\left(2\sqrt{6}\right)^2-2.2\sqrt{6}.1+1^2}=\sqrt{\left(2\sqrt{6}-1\right)^2}\)
\(=\left|2\sqrt{6}-1\right|=2\sqrt{6}-1\)
29.\(\sqrt{14-8\sqrt{3}}=\sqrt{14-2\sqrt{48}}=\sqrt{\left(\sqrt{8}\right)^2-2\sqrt{6}.\sqrt{8}+\left(\sqrt{6}\right)^2}\)
\(=\sqrt{\left(\sqrt{8}-\sqrt{6}\right)^2}=\left|\sqrt{8}-\sqrt{6}\right|=\sqrt{8}-\sqrt{6}\)
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57.\(\sqrt{8-\sqrt{55}}=\sqrt{\dfrac{16-2.\sqrt{5}.\sqrt{11}}{2}}=\sqrt{\dfrac{\sqrt{11}^2-2.\sqrt{5}.\sqrt{11}+\left(\sqrt{5}\right)^2}{2}}\)
\(=\sqrt{\dfrac{\left(\sqrt{11}-\sqrt{5}\right)^2}{2}}=\dfrac{\left|\sqrt{11}-\sqrt{5}\right|}{\sqrt{2}}=\dfrac{\sqrt{11}-\sqrt{5}}{\sqrt{2}}\)
58. \(\sqrt{7+\sqrt{33}}=\sqrt{\dfrac{14+2\sqrt{3}.\sqrt{11}}{2}}=\sqrt{\dfrac{\left(\sqrt{11}\right)^2+2\sqrt{3}.\sqrt{11}+\left(\sqrt{3}\right)^2}{2}}\)
\(=\sqrt{\dfrac{\left(\sqrt{11}+\sqrt{3}\right)^2}{2}}=\dfrac{\left|\sqrt{11}+\sqrt{3}\right|}{\sqrt{2}}=\dfrac{\sqrt{11}+\sqrt{3}}{\sqrt{2}}\)
mấy câu dưới bạn cũng làm tương tự thôi
60) \(\sqrt{7-3\sqrt{5}}=\dfrac{\sqrt{14-6\sqrt{5}}}{\sqrt{2}}=\dfrac{3-\sqrt{5}}{\sqrt{2}}=\dfrac{3\sqrt{2}-\sqrt{10}}{2}\)
61) \(\sqrt{23+3\sqrt{5}}=\dfrac{\sqrt{46+6\sqrt{5}}}{\sqrt{2}}=\dfrac{3\sqrt{5}+1}{\sqrt{2}}=\dfrac{3\sqrt{10}+\sqrt{2}}{2}\)
62) \(\sqrt{7-\sqrt{33}}=\dfrac{\sqrt{14-2\sqrt{33}}}{\sqrt{2}}=\dfrac{\sqrt{11}-\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{22}-\sqrt{6}}{2}\)
63) \(\sqrt{8+\sqrt{55}}=\dfrac{\sqrt{16+2\sqrt{55}}}{\sqrt{2}}=\dfrac{\sqrt{11}+\sqrt{5}}{\sqrt{2}}=\dfrac{\sqrt{22}+\sqrt{10}}{2}\)
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\(a.\dfrac{11}{10}\text{=}\dfrac{11\times3}{10\times3}\text{=}\dfrac{33}{30}\)
\(\dfrac{19}{30}\) giữ nguyên
\(b.\dfrac{23}{38}\text{=}\dfrac{23\times3}{38\times3}\text{=}\dfrac{69}{114}\)
\(\dfrac{14}{57}\text{=}\dfrac{14\times2}{57\times2}\text{=}\dfrac{28}{114}\)
help me
\(=\dfrac{20}{19}+\dfrac{11}{38}=\dfrac{51}{38}\)