THỰC HIỆN PHÉP TÍNH:

22) \(\frac{1}{\sqrt{5}+\sqrt{2}}+\frac{1}{\sqrt{5}-\sqrt{2}}\)

23) \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

24) \(\frac{\sqrt{18}}{\sqrt{2}}-\frac{\sqrt{12}}{\sqrt{3}}\)

25) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

27) \(\sqrt{3-2\sqrt{2}}\)

28) \(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-2\sqrt{2}\)

30) \(\left(2\sqrt{1\frac{9}{16}}-\sqrt{5\frac{1}{16}}\right):\sqrt{16}\)

34) \(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)

35) \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right).3\sqrt{6}\)

36) \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

39) \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}}\)

45) \(\frac{\sqrt{6-2\sqrt{5}}}{2-\sqrt{20}}\)

a) ^{_{\(\frac{2\sqrt{5}-4\sqrt{10}}{3\sqrt{10}}\)}}

b)\(\frac{6\sqrt{6}-2\sqrt{12}+3-\sqrt{2}}{2\sqrt{6}+1}\)

c)\(\frac{\sqrt{3\left(3-\sqrt{11}\right)^2}}{\sqrt{6}\left(3-\sqrt{11}\right)}\)

d)\(\frac{5\sqrt{7}-4\sqrt{35}+7\sqrt{5}}{\sqrt{35}}\)

e) \(\left(\sqrt{3}-1\right)\sqrt{2\sqrt{19+8\sqrt{3}-4}}\)

g) \(\sqrt{47+\sqrt{5}}.\sqrt{7-\sqrt{2+\sqrt{5}}.}\sqrt{7+\sqrt{2+\sqrt{5}}}\)

bài 5

ĐK:\(x>2,y>1\)

\(\frac{36}{\sqrt{x-2}}+\frac{4}{\sqrt{y-1}}=28-4\sqrt{x-2}-\sqrt{y-1}..\)\(\Leftrightarrow\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}+\frac{4}{\sqrt{y-1}}+\sqrt{y-1}=28\)

Áp dụng AM-GM ta có:

\(\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}\ge2\sqrt{\frac{144\sqrt{x-2}}{\sqrt{x-2}}}=24\)

\(\frac{4}{\sqrt{y-1}}+\sqrt{y-1}\ge2\sqrt{\frac{4\sqrt{y-1}}{\sqrt{y-1}}}=4.\)

\(\Rightarrow\frac{36}{\sqrt{x-2}}+4\sqrt{x-2}+\frac{4}{\sqrt{y-1}}+\sqrt{y-1}\ge28.\)

Dấu \(=\)xảy ra khi \(\frac{36}{\sqrt{x-2}}=4\sqrt{x-2}\Leftrightarrow x=11\left(n\right).\)

\(\frac{4}{\sqrt{y-1}}=\sqrt{y-1}\Leftrightarrow y=5\left(n\right).\)

Vậy \(x=11,y=5\)

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=\(\sqrt{5}\)

bài 1 So sánh

a, \(\sqrt{50}+\sqrt{39}+3\) và 16

b, \(\sqrt{3}+\sqrt{8}+2\) và 7

c, \(2\sqrt{26}+3\sqrt{64}-5\) và 28

bài 2 Tính nhanh

a, \(\sqrt{4}+\sqrt{25}+\sqrt{64}+...+\sqrt{2500}\)

b, \(\sqrt{1}+\sqrt{25}+\sqrt{81}+...+\sqrt{9409}\)

c, \(\sqrt{\frac{1}{4}}+\sqrt{\frac{1}{36}}+\sqrt{\frac{1}{144}}+...+\sqrt{\frac{1}{9900^2}}\)