a: \(\sqrt{5+2\sqrt{6}}=\sqrt{3}+\sqrt{2}\)

b: \(\sqrt{12+2\sqrt{35}}-\sqrt{12-2\sqrt{35}}=\sqrt{7}+\sqrt{5}-\sqrt{7}+\sqrt{5}=2\sqrt{5}\)

c: \(\sqrt{16+6\sqrt{7}}=4+\sqrt{7}\)

d: \(\sqrt{31-12\sqrt{3}}=3\sqrt{3}-2\)

e: \(\sqrt{27+10\sqrt{2}}=5+\sqrt{2}\)

f: \(\sqrt{14+6\sqrt{5}}=3+\sqrt{5}\)

A = 0,(36) - 0,(71)

= 36/99 - 71/99

= -35/99

B = [3,(12) - 2,(5)] : 0,(14)

= (103/33 - 203/99) : 14/99

= 106/99 : 14/99

= 53/7

\(A=0,\left(36\right)-0,\left(71\right)\)

\(A=\dfrac{36}{99}-\dfrac{71}{99}=-\dfrac{35}{99}=-0,\left(35\right)\)

\(B=\left[3,\left(12\right)-2,\left(5\right)\right]:0,\left(14\right)\)

\(B=\left(\dfrac{3\cdot99+12}{99}-\dfrac{2\cdot9+5}{9}\right):\dfrac{14}{99}\)

\(B=\left(\dfrac{309}{99}-\dfrac{23}{9}\right):\dfrac{14}{99}\)

\(B=\dfrac{56}{99}:\dfrac{14}{99}\)

\(B=4\)

A=0,(36)-0,(71)

A=\(\dfrac{4}{11}\)-\(\dfrac{71}{99}\)

A=\(\dfrac{-35}{99}\)

B=[3,(12)-2,(5)]:0,(14)

B=[\(\dfrac{103}{33}\)-\(\dfrac{23}{9}\)]:\(\dfrac{14}{99}\)

B=\(\dfrac{-50}{33}\):\(\dfrac{14}{99}\)

B=\(\dfrac{-75}{7}\)

\(\frac{\sqrt{12}-\sqrt{30}}{\sqrt{6}}\cdot\frac{\sqrt{35}+\sqrt{14}}{\sqrt{7}}\)

\(=\frac{2\sqrt{3}-\sqrt{30}}{\sqrt{6}}\cdot\frac{\sqrt{35}+\sqrt{14}}{\sqrt{7}}\)

\(=\frac{\left(2\sqrt{3}-\sqrt{30}\right)\cdot\left(\sqrt{35}+\sqrt{14}\right)}{\sqrt{6}\cdot\sqrt{7}}\)

\(=\frac{\left(2\sqrt{3}-\sqrt{30}\right)\cdot\left(\sqrt{35}+\sqrt{14}\right)}{\sqrt{42}}\)

\(=\frac{2\sqrt{3}\cdot\sqrt{35}+2\sqrt{3}\cdot\sqrt{14}-\sqrt{30}\cdot\sqrt{35}-\sqrt{30}\cdot\sqrt{14}}{\sqrt{42}}\)

\(=\frac{2\sqrt{105}+2\sqrt{42}-5\sqrt{42}-2\sqrt{105}}{\sqrt{42}}\)

\(=\frac{-3\sqrt{42}}{\sqrt{42}}=-3\)

\(=\frac{\sqrt{2}.\sqrt{6}-\sqrt{5}.\sqrt{6}}{\sqrt{6}}.\frac{\sqrt{5}.\sqrt{7}+\sqrt{2}.\sqrt{7}}{\sqrt{7}}\)

\(=\left(\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)=2-5=-3\)

AI

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AI

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MINH

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\(E=2.3+3.4+4.5+3.6+2.7+4.15=2\left(3+7\right)+3\left(4+6\right)+4\left(5+15\right)=2.10+3.10+4.20=20+30+80=130\)

\(F=3\left(12+13+14+15\right)+3\left(8+7+6+5\right)=3\left(12+8+13+7+14+6+15+5\right)=3\left(20+20+20+20\right)=3.80=240\)

f: Ta có: \(E=3\cdot\left(12+13+14+15\right)+3\left(8+7+6+5\right)\)

\(=3\left(12+13+14+15+8+7+6+5\right)\)

\(=3\cdot80=240\)

\(A=\dfrac{2}{20.12}+\dfrac{2}{12.14}+\dfrac{2}{14.16}+...+\dfrac{2}{98.100}\)

\(A=\dfrac{1}{10}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{16}+...+\dfrac{1}{98}-\dfrac{1}{100}\)

\(A=\dfrac{1}{10}-\dfrac{1}{100}\)

\(A=\dfrac{9}{100}\)

A=1/10−1/12+1/12−1/14+1/14−1/16+...+1/98−1/100

A=9/CHO TUI XIN 1 LIKE NHA

a) \(=2\sqrt{5}-3\sqrt{5}+\sqrt{5}-1=-1\)

b) \(=\left[\sqrt{14}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right].\sqrt{\left(\sqrt{\dfrac{7}{2}}-\sqrt{\dfrac{3}{2}}\right)^2}\)

\(=\left(\sqrt{14}+\sqrt{6}\right)\left(\sqrt{\dfrac{7}{2}}-\sqrt{\dfrac{3}{2}}\right)\)

\(=\sqrt{49}-\sqrt{21}+\sqrt{21}-\sqrt{9}\)

\(=7-3=4\)

a) \(\sqrt{20}-15\sqrt{\dfrac{1}{5}}+\sqrt{\left(1-\sqrt{5}\right)^2}=2\sqrt{5}-3\sqrt{5}+\sqrt{5}-1=-1\)

b) \(\left(\dfrac{14}{\sqrt{14}}+\dfrac{\sqrt{12}+\sqrt{30}}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}=\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}=\left(\sqrt{7}+\sqrt{3}\right)\sqrt{10-2\sqrt{21}}=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)=4\)

a) \(\sqrt{25x}\) = 35 

b) \(\sqrt{4x}\)<= 162

 c) \(3\sqrt{x}\) = √12

 d) \(2\sqrt{x}\) >=10
 

Đùa ak :)