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1. ![sqrt{35} textless 6 \ 5 sqrt{6} textgreater 4 sqrt{7} sqrt{35} textless 6 \ 5 sqrt{6} textgreater 4 sqrt{7}](https://tex.z-dn.net/?f=+sqrt%7B35%7D++textless+++6+%5C++5+sqrt%7B6%7D++textgreater+++4+sqrt%7B7%7D+)
2.![= 0,4 sqrt{2500} + 13 = 0,4*50 + 13 = 33 = 0,4 sqrt{2500} + 13 = 0,4*50 + 13 = 33](https://tex.z-dn.net/?f=%3D+0%2C4++sqrt%7B2500%7D+%2B+13+%3D+0%2C4%2A50+%2B+13+%3D+33)
![= sqrt{6*4} - 4 sqrt{6} + sqrt{9*6} = 2 sqrt{6 } - 4 sqrt{6} + 3 sqrt{6} = sqrt{6} = sqrt{6*4} - 4 sqrt{6} + sqrt{9*6} = 2 sqrt{6 } - 4 sqrt{6} + 3 sqrt{6} = sqrt{6}](https://tex.z-dn.net/?f=%3D++sqrt%7B6%2A4%7D+-+4+sqrt%7B6%7D+%2B++sqrt%7B9%2A6%7D+%3D+2+sqrt%7B6+%7D++-+4+sqrt%7B6%7D+%2B+3++sqrt%7B6%7D+%3D++sqrt%7B6%7D+)
3.![= ( 3^{2} - ( sqrt{7}) ^{2}) = 9 - 7 = 2 = ( 3^{2} - ( sqrt{7}) ^{2}) = 9 - 7 = 2](https://tex.z-dn.net/?f=%3D+%28+3%5E%7B2%7D+-+%28+sqrt%7B7%7D%29+%5E%7B2%7D%29+%3D+9+-+7+%3D+2)
![= 3( sqrt{2} ) ^{2} + sqrt{50*2} = 3*2 +10= 16 = 3( sqrt{2} ) ^{2} + sqrt{50*2} = 3*2 +10= 16](https://tex.z-dn.net/?f=%3D+3%28+sqrt%7B2%7D+%29+%5E%7B2%7D+%2B++sqrt%7B50%2A2%7D+%3D+3%2A2+%2B10%3D+16)
![= 6^{2} - 12sqrt{3} + ( sqrt{3} ) ^{2} = 36 - 12 sqrt{3} +3 = 39 - 12 sqrt{3} = 6^{2} - 12sqrt{3} + ( sqrt{3} ) ^{2} = 36 - 12 sqrt{3} +3 = 39 - 12 sqrt{3}](https://tex.z-dn.net/?f=%3D++6%5E%7B2%7D+-++12sqrt%7B3%7D+%2B+%28+sqrt%7B3%7D+%29+%5E%7B2%7D+%3D+36+-+12+sqrt%7B3%7D+%2B3+%3D+39+-+12+sqrt%7B3%7D+)
![= 10 sqrt{3} - 4 sqrt{16*3} - sqrt{25*3} = 10 sqrt{3} - 16 sqrt{3} - 5 sqrt{3}= - 11 sqrt{3} = 10 sqrt{3} - 4 sqrt{16*3} - sqrt{25*3} = 10 sqrt{3} - 16 sqrt{3} - 5 sqrt{3}= - 11 sqrt{3}](https://tex.z-dn.net/?f=%3D+10+sqrt%7B3%7D+-+4++sqrt%7B16%2A3%7D+-++sqrt%7B25%2A3%7D+%3D+10+sqrt%7B3%7D+-+16+sqrt%7B3%7D+-+5+sqrt%7B3%7D%3D+-+11+sqrt%7B3%7D+)
4.![= frac{(2- sqrt{c})(2+ sqrt{c)} } { sqrt{c} (2+ sqrt{c)} } = frac{(2- sqrt{c)}} { sqrt{c} } = frac{ sqrt{c}(2- sqrt{c)} } {(sqrt{c} )^{2} } = frac{2 sqrt{c} - c } {c} = frac{(2- sqrt{c})(2+ sqrt{c)} } { sqrt{c} (2+ sqrt{c)} } = frac{(2- sqrt{c)}} { sqrt{c} } = frac{ sqrt{c}(2- sqrt{c)} } {(sqrt{c} )^{2} } = frac{2 sqrt{c} - c } {c}](https://tex.z-dn.net/?f=%3D++frac%7B%282-+sqrt%7Bc%7D%29%282%2B+sqrt%7Bc%29%7D+%7D+%7B+sqrt%7Bc%7D+%282%2B+sqrt%7Bc%29%7D++%7D++%3D++frac%7B%282-+sqrt%7Bc%29%7D%7D+++%7B+sqrt%7Bc%7D+%7D+%3D++frac%7B++sqrt%7Bc%7D%282-+sqrt%7Bc%29%7D+++%7D++++%7B%28sqrt%7Bc%7D+%29%5E%7B2%7D+%7D+%3D++frac%7B2+sqrt%7Bc%7D+-+c+%7D++++%7Bc%7D+)
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