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29)
![a \sqrt{49a^2x} +2a^2 \sqrt{9x} - \sqrt{121a^4x} = \\ =a \sqrt{7^2a^2x} +2a^2 \sqrt{3^2x} - \sqrt{11^2(a^2)^2x}=\\ =a*7*a \sqrt{x} +2a^2*3 \sqrt{x} - 11*a^2\sqrt{x}=\\ =7a^2 \sqrt{x} +6a^2 \sqrt{x} - 11a^2\sqrt{x}=(7a^2+6a^2-11a^2) \sqrt{x} = \\ =2a^2 \sqrt{x} a \sqrt{49a^2x} +2a^2 \sqrt{9x} - \sqrt{121a^4x} = \\ =a \sqrt{7^2a^2x} +2a^2 \sqrt{3^2x} - \sqrt{11^2(a^2)^2x}=\\ =a*7*a \sqrt{x} +2a^2*3 \sqrt{x} - 11*a^2\sqrt{x}=\\ =7a^2 \sqrt{x} +6a^2 \sqrt{x} - 11a^2\sqrt{x}=(7a^2+6a^2-11a^2) \sqrt{x} = \\ =2a^2 \sqrt{x}](https://tex.z-dn.net/?f=a+%5Csqrt%7B49a%5E2x%7D+%2B2a%5E2+%5Csqrt%7B9x%7D+-+%5Csqrt%7B121a%5E4x%7D+%3D+%5C%5C+%3Da+%5Csqrt%7B7%5E2a%5E2x%7D+%2B2a%5E2+%5Csqrt%7B3%5E2x%7D+-+%5Csqrt%7B11%5E2%28a%5E2%29%5E2x%7D%3D%5C%5C+%3Da%2A7%2Aa+%5Csqrt%7Bx%7D+%2B2a%5E2%2A3+%5Csqrt%7Bx%7D+-+11%2Aa%5E2%5Csqrt%7Bx%7D%3D%5C%5C+%3D7a%5E2+%5Csqrt%7Bx%7D+%2B6a%5E2+%5Csqrt%7Bx%7D+-+11a%5E2%5Csqrt%7Bx%7D%3D%287a%5E2%2B6a%5E2-11a%5E2%29+%5Csqrt%7Bx%7D+%3D+%5C%5C+%3D2a%5E2+%5Csqrt%7Bx%7D+)
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![2m^2 \sqrt{18mn^3} -3 \sqrt{50m^5n^3} +9mn \sqrt{2m^3n} = \\ =2m^2 \sqrt{9*2*mn^2n} -3 \sqrt{25*2*m^2m^2mn^2n} +9mn \sqrt{2*m^2mn} = \\= 2m^2 \sqrt{3^2*2*mn^2n} -3 \sqrt{5^2*2*m^2m^2mn^2n} +9mn \sqrt{2*m^2mn} = \\= 2m^2*3*n \sqrt{2*mn} -3*5mmn\sqrt{2*mn} +9mnm \sqrt{2*mn} = \\ = 6m^2n \sqrt{2mn} -15m^2n\sqrt{2mn} +9m^2n \sqrt{2mn} = \\ =(6-15+9)m^2n \sqrt{2mn} =(0)*m^2n \sqrt{2mn}=0 2m^2 \sqrt{18mn^3} -3 \sqrt{50m^5n^3} +9mn \sqrt{2m^3n} = \\ =2m^2 \sqrt{9*2*mn^2n} -3 \sqrt{25*2*m^2m^2mn^2n} +9mn \sqrt{2*m^2mn} = \\= 2m^2 \sqrt{3^2*2*mn^2n} -3 \sqrt{5^2*2*m^2m^2mn^2n} +9mn \sqrt{2*m^2mn} = \\= 2m^2*3*n \sqrt{2*mn} -3*5mmn\sqrt{2*mn} +9mnm \sqrt{2*mn} = \\ = 6m^2n \sqrt{2mn} -15m^2n\sqrt{2mn} +9m^2n \sqrt{2mn} = \\ =(6-15+9)m^2n \sqrt{2mn} =(0)*m^2n \sqrt{2mn}=0](https://tex.z-dn.net/?f=2m%5E2+%5Csqrt%7B18mn%5E3%7D+-3+%5Csqrt%7B50m%5E5n%5E3%7D+%2B9mn+%5Csqrt%7B2m%5E3n%7D+%3D+%5C%5C+%3D2m%5E2+%5Csqrt%7B9%2A2%2Amn%5E2n%7D+-3+%5Csqrt%7B25%2A2%2Am%5E2m%5E2mn%5E2n%7D+%2B9mn+%5Csqrt%7B2%2Am%5E2mn%7D+%3D+%5C%5C%3D++2m%5E2+%5Csqrt%7B3%5E2%2A2%2Amn%5E2n%7D+-3+%5Csqrt%7B5%5E2%2A2%2Am%5E2m%5E2mn%5E2n%7D+%2B9mn+%5Csqrt%7B2%2Am%5E2mn%7D+%3D+%5C%5C%3D++2m%5E2%2A3%2An+%5Csqrt%7B2%2Amn%7D+-3%2A5mmn%5Csqrt%7B2%2Amn%7D+%2B9mnm+%5Csqrt%7B2%2Amn%7D+%3D+%5C%5C+%3D++6m%5E2n+%5Csqrt%7B2mn%7D+-15m%5E2n%5Csqrt%7B2mn%7D+%2B9m%5E2n+%5Csqrt%7B2mn%7D+%3D+%5C%5C+%3D%286-15%2B9%29m%5E2n+%5Csqrt%7B2mn%7D+%3D%280%29%2Am%5E2n+%5Csqrt%7B2mn%7D%3D0)
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![3y \sqrt[3]{8x^5y} +3 \sqrt[3]{x^5y^4} -4x \sqrt[3]{x^2y^4} = \\ =3y \sqrt[3]{2^3x^3x^2y} +3 \sqrt[3]{x^3x^2y^3y} -4x \sqrt[3]{x^2y^3y}= \\ =3y*2*x \sqrt[3]{x^2y} +3*x*y \sqrt[3]{x^2y} -4x*y \sqrt[3]{x^2y}= \\ =6xy \sqrt[3]{x^2y} +3xy \sqrt[3]{x^2y} -4xy \sqrt[3]{x^2y}= \\ =(6+3-4)xy \sqrt[3]{x^2y}=(5)xy \sqrt[3]{x^2y}=5xy \sqrt[3]{x^2y} 3y \sqrt[3]{8x^5y} +3 \sqrt[3]{x^5y^4} -4x \sqrt[3]{x^2y^4} = \\ =3y \sqrt[3]{2^3x^3x^2y} +3 \sqrt[3]{x^3x^2y^3y} -4x \sqrt[3]{x^2y^3y}= \\ =3y*2*x \sqrt[3]{x^2y} +3*x*y \sqrt[3]{x^2y} -4x*y \sqrt[3]{x^2y}= \\ =6xy \sqrt[3]{x^2y} +3xy \sqrt[3]{x^2y} -4xy \sqrt[3]{x^2y}= \\ =(6+3-4)xy \sqrt[3]{x^2y}=(5)xy \sqrt[3]{x^2y}=5xy \sqrt[3]{x^2y}](https://tex.z-dn.net/?f=3y+%5Csqrt%5B3%5D%7B8x%5E5y%7D+%2B3+%5Csqrt%5B3%5D%7Bx%5E5y%5E4%7D+-4x+%5Csqrt%5B3%5D%7Bx%5E2y%5E4%7D+%3D+%5C%5C+%3D3y+%5Csqrt%5B3%5D%7B2%5E3x%5E3x%5E2y%7D+%2B3+%5Csqrt%5B3%5D%7Bx%5E3x%5E2y%5E3y%7D+-4x+%5Csqrt%5B3%5D%7Bx%5E2y%5E3y%7D%3D+%5C%5C+%3D3y%2A2%2Ax+%5Csqrt%5B3%5D%7Bx%5E2y%7D+%2B3%2Ax%2Ay+%5Csqrt%5B3%5D%7Bx%5E2y%7D+-4x%2Ay+%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D+%5C%5C+%3D6xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D+%2B3xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D+-4xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D+%5C%5C+%3D%286%2B3-4%29xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D%285%29xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D%3D5xy+%5Csqrt%5B3%5D%7Bx%5E2y%7D)
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thomasdamian22:
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