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1)
a.
![3 sqrt{1 frac{11}{25} } -1=3 sqrt{ frac{36}{25} } -1=3* frac{6}{5} -1=2 frac{3}{5} 3 sqrt{1 frac{11}{25} } -1=3 sqrt{ frac{36}{25} } -1=3* frac{6}{5} -1=2 frac{3}{5}](https://tex.z-dn.net/?f=3+sqrt%7B1+frac%7B11%7D%7B25%7D+%7D+-1%3D3+sqrt%7B+frac%7B36%7D%7B25%7D+%7D+-1%3D3%2A+frac%7B6%7D%7B5%7D+-1%3D2+frac%7B3%7D%7B5%7D+)
б.
![sqrt{0.08} * sqrt{2} = sqrt{0.08*2} = sqrt{0.16} =0.4 sqrt{0.08} * sqrt{2} = sqrt{0.08*2} = sqrt{0.16} =0.4](https://tex.z-dn.net/?f=+sqrt%7B0.08%7D+%2A+sqrt%7B2%7D+%3D+sqrt%7B0.08%2A2%7D+%3D+sqrt%7B0.16%7D+%3D0.4)
в.
![frac{ sqrt{125} }{ sqrt{5} } = sqrt{ frac{125}{5} } = sqrt{25} =5 frac{ sqrt{125} }{ sqrt{5} } = sqrt{ frac{125}{5} } = sqrt{25} =5](https://tex.z-dn.net/?f=+frac%7B+sqrt%7B125%7D+%7D%7B+sqrt%7B5%7D+%7D+%3D+sqrt%7B+frac%7B125%7D%7B5%7D+%7D+%3D+sqrt%7B25%7D+%3D5)
г.
![sqrt{2^4*3^4} = sqrt{2^4} * sqrt{3^4} =2^2*3^2=36 sqrt{2^4*3^4} = sqrt{2^4} * sqrt{3^4} =2^2*3^2=36](https://tex.z-dn.net/?f=+sqrt%7B2%5E4%2A3%5E4%7D+%3D+sqrt%7B2%5E4%7D+%2A+sqrt%7B3%5E4%7D+%3D2%5E2%2A3%5E2%3D36)
2)
а.
![2x^2+7x-9=0 2x^2+7x-9=0](https://tex.z-dn.net/?f=2x%5E2%2B7x-9%3D0)
![D=49-4*2(-9)=121 D=49-4*2(-9)=121](https://tex.z-dn.net/?f=D%3D49-4%2A2%28-9%29%3D121)
![x_{1} = frac{-7+11}{4} =1 x_{1} = frac{-7+11}{4} =1](https://tex.z-dn.net/?f=+x_%7B1%7D+%3D+frac%7B-7%2B11%7D%7B4%7D+%3D1)
![x_{2} = frac{-7-11}{4}=-4.5 x_{2} = frac{-7-11}{4}=-4.5](https://tex.z-dn.net/?f=+x_%7B2%7D+%3D+frac%7B-7-11%7D%7B4%7D%3D-4.5+)
б.
![3x^2=18x 3x^2=18x](https://tex.z-dn.net/?f=3x%5E2%3D18x)
![x^2=6x x^2=6x](https://tex.z-dn.net/?f=x%5E2%3D6x)
![x^2-6x=0 x^2-6x=0](https://tex.z-dn.net/?f=x%5E2-6x%3D0)
![x(x-6)=0 x(x-6)=0](https://tex.z-dn.net/?f=x%28x-6%29%3D0)
![x_{1} =0 x_{1} =0](https://tex.z-dn.net/?f=+x_%7B1%7D+%3D0)
![x_{2} =6 x_{2} =6](https://tex.z-dn.net/?f=+x_%7B2%7D+%3D6)
в.
![100 x^{2} -16=0 100 x^{2} -16=0](https://tex.z-dn.net/?f=100+x%5E%7B2%7D+-16%3D0)
![100x^{2} = 16 100x^{2} = 16](https://tex.z-dn.net/?f=+100x%5E%7B2%7D+%3D+16)
![x^{2} = frac{16}{100} x^{2} = frac{16}{100}](https://tex.z-dn.net/?f=+x%5E%7B2%7D+%3D+frac%7B16%7D%7B100%7D+)
![x_{1} = sqrt{ frac{16}{100} } = frac{4}{10} =0.4 x_{1} = sqrt{ frac{16}{100} } = frac{4}{10} =0.4](https://tex.z-dn.net/?f=+x_%7B1%7D+%3D+sqrt%7B+frac%7B16%7D%7B100%7D+%7D+%3D+frac%7B4%7D%7B10%7D+%3D0.4)
![x_{2} =-0.4 x_{2} =-0.4](https://tex.z-dn.net/?f=+x_%7B2%7D+%3D-0.4)
г.
![x^{2} -16x+63=0 x^{2} -16x+63=0](https://tex.z-dn.net/?f=+x%5E%7B2%7D+-16x%2B63%3D0)
![D=256-4*63=4 D=256-4*63=4](https://tex.z-dn.net/?f=D%3D256-4%2A63%3D4)
![x_{1} = frac{16+2}{2} =9 x_{1} = frac{16+2}{2} =9](https://tex.z-dn.net/?f=+x_%7B1%7D+%3D+frac%7B16%2B2%7D%7B2%7D+%3D9)
![x_{2} = frac{16-2}{2} =7 x_{2} = frac{16-2}{2} =7](https://tex.z-dn.net/?f=+x_%7B2%7D+%3D+frac%7B16-2%7D%7B2%7D+%3D7)
3)
а.
![3 sqrt{50} - sqrt{98} =3 sqrt{25*2} - sqrt{49*2} =15 sqrt{2} -7 sqrt{2} =8 sqrt{2} 3 sqrt{50} - sqrt{98} =3 sqrt{25*2} - sqrt{49*2} =15 sqrt{2} -7 sqrt{2} =8 sqrt{2}](https://tex.z-dn.net/?f=3+sqrt%7B50%7D+-+sqrt%7B98%7D+%3D3+sqrt%7B25%2A2%7D+-+sqrt%7B49%2A2%7D+%3D15+sqrt%7B2%7D+-7+sqrt%7B2%7D+%3D8+sqrt%7B2%7D+)
б.
![(2 sqrt{3} - sqrt{27} ) sqrt{3} =2*3- sqrt{27*3} =6- sqrt{81} =6-9=-3 (2 sqrt{3} - sqrt{27} ) sqrt{3} =2*3- sqrt{27*3} =6- sqrt{81} =6-9=-3](https://tex.z-dn.net/?f=%282+sqrt%7B3%7D+-+sqrt%7B27%7D+%29+sqrt%7B3%7D+%3D2%2A3-+sqrt%7B27%2A3%7D+%3D6-+sqrt%7B81%7D+%3D6-9%3D-3)
в.
![(4- sqrt{5})^2=(4- sqrt{5} )(4- sqrt{5})=16-8 sqrt{5} +5=21-8 sqrt{5} (4- sqrt{5})^2=(4- sqrt{5} )(4- sqrt{5})=16-8 sqrt{5} +5=21-8 sqrt{5}](https://tex.z-dn.net/?f=%284-+sqrt%7B5%7D%29%5E2%3D%284-+sqrt%7B5%7D++%29%284-+sqrt%7B5%7D%29%3D16-8+sqrt%7B5%7D++%2B5%3D21-8+sqrt%7B5%7D+)
4)
а.
![frac{2+ sqrt{2} }{ sqrt{3}+ sqrt{6} } = frac{ sqrt{2}( sqrt{2}+1) }{ sqrt{3}(1+ sqrt{2} ) } = frac{ sqrt{2} }{ sqrt{3} } frac{2+ sqrt{2} }{ sqrt{3}+ sqrt{6} } = frac{ sqrt{2}( sqrt{2}+1) }{ sqrt{3}(1+ sqrt{2} ) } = frac{ sqrt{2} }{ sqrt{3} }](https://tex.z-dn.net/?f=+frac%7B2%2B+sqrt%7B2%7D+%7D%7B+sqrt%7B3%7D%2B+sqrt%7B6%7D++%7D+%3D+frac%7B+sqrt%7B2%7D%28+sqrt%7B2%7D%2B1%29++%7D%7B+sqrt%7B3%7D%281%2B+sqrt%7B2%7D+%29+%7D+%3D+frac%7B+sqrt%7B2%7D+%7D%7B+sqrt%7B3%7D+%7D+)
б.
![frac{9-a}{ sqrt{a}-3 } = frac{(3- sqrt{a})(3+ sqrt{a} ) }{-1(3- sqrt{a}) } =-3- sqrt{a} frac{9-a}{ sqrt{a}-3 } = frac{(3- sqrt{a})(3+ sqrt{a} ) }{-1(3- sqrt{a}) } =-3- sqrt{a}](https://tex.z-dn.net/?f=+frac%7B9-a%7D%7B+sqrt%7Ba%7D-3+%7D+%3D+frac%7B%283-+sqrt%7Ba%7D%29%283%2B+sqrt%7Ba%7D+%29+%7D%7B-1%283-+sqrt%7Ba%7D%29+%7D+%3D-3-+sqrt%7Ba%7D+)
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