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\(\sqrt{16-6\sqrt{7}}\\ =\sqrt{9-6\sqrt{7}+7}\\ =\sqrt{3^2-2.3.\sqrt{7}+\left(\sqrt{7}\right)^2}\\=\sqrt{\left(3-\sqrt{7}\right)^2}\\ =\left|3-\sqrt{7}\right|\\ =3-\sqrt{7}\)
a.\(\sqrt{\frac{289+4\sqrt{72}}{16}}+\sqrt{\frac{129}{16}+\sqrt{2}}\)
b. \(\sqrt{16-6\sqrt{7}}+\sqrt{10-2\sqrt{21}}\)
c. \(\sqrt{28+\sqrt{300}}+\sqrt{19-\sqrt{192}}\)
\(a,\sqrt{3+2\sqrt{2}}-\sqrt{2}\)
\(b,\sqrt{16-6\sqrt{7}}-2\sqrt{7}\)
\(c,\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{6}}\)
\(d,\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
\(e,\sqrt{\left(-2\right)^6}+\sqrt{\left(-3\right)^4}\)
1.\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
2.\(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
3. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
4.\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
5.\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
6.\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
7.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
Rút gọn
a,\(\sqrt{14+4\sqrt{3}.\sqrt{2}}\)
b,\(\sqrt{11-4\sqrt{3}.\sqrt{2}}\)
c,\(\sqrt{28+16\sqrt{3}}\)
d,\(\sqrt{11+4\sqrt{7}}\)
e,\(\sqrt{29-4\sqrt{7}}\)
f,\(\sqrt{21+6\sqrt{2}.\sqrt{3}}\)
\(\sqrt{4\sqrt{2}-\sqrt{4+16\sqrt{6-4\sqrt{2}}}}+\sqrt{\sqrt{3}+\sqrt{228+50\sqrt{67-16\sqrt{3}}}}\)
Viết các biểu thức sau dưới dạng bình phương một tổng hoặc một hiệu :
1) \(5-2\sqrt{6}\)
2) \(8+2\sqrt{15}\)
3) \(10-2\sqrt{21}\)
4) \(21+6\sqrt{6}\)
5) \(14+8\sqrt{3}\)
6) \(36-12\sqrt{5}\)
7) \(25+4\sqrt{6}\)
8) \(98-16\sqrt{3}\)
1)chứng minh
a)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
b)\(\sqrt{11+6\sqrt{2}}+\sqrt{11-6\sqrt{2}}=6\)
2)chứng minh
a)\(8-2\sqrt{7}=\left(\sqrt{7}-1\right)^2\)
b)\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=2\)
bài 1: thực hiện phép tính
a, (\(\sqrt{12}+3\sqrt{15}-4\sqrt{135}\)).\(\sqrt{3}\)
b, A=\(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
c, \(\frac{9\sqrt{5^2+3\sqrt{27}}}{\sqrt{5}+\sqrt{3}}\)
d, \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
e, (\(\sqrt{12}+\sqrt{15}+\sqrt{27}\)):\(\sqrt{15}\)
f, (12\(\sqrt{50}-8\sqrt{200}+7\sqrt{450}\)):\(\sqrt{10}\)
g, (\(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+\sqrt{\frac{9}{7}}\)):\(\sqrt{7}\)
bài 2:rút gọn rồi tính các giá trị biểu thức
a, A= \(\sqrt{\frac{\left(x-6\right)^4}{\left(5-x\right)^2}}\)+\(\frac{x^2-36}{x-5}\) (x<5) tại x=4
b, B=5x-\(\sqrt{125}\)+\(\frac{\sqrt{x^3+5x^2}}{\sqrt{x+5}}\) (x ≥ 0)tại x=\(\sqrt{5}\)
Tính:
a/ \(\sqrt{8+2\sqrt{15}}+\frac{2}{\sqrt{5}+\sqrt{3}}\)
b/ \(\sqrt{7+2\sqrt{6}}+\frac{6-2\sqrt{6}}{\sqrt{6}}-\sqrt{54}\)
