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Vikach2014
@Vikach2014
August 2022
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СРОЧНО!!!
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Answers & Comments
1)![\displaystyle (-2*\sqrt[4]{7})^{4}=(-2)^{4}*7^{\frac{1}{4}*4 } =16*7= 112 \displaystyle (-2*\sqrt[4]{7})^{4}=(-2)^{4}*7^{\frac{1}{4}*4 } =16*7= 112](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%28-2%2A%5Csqrt%5B4%5D%7B7%7D%29%5E%7B4%7D%3D%28-2%29%5E%7B4%7D%2A7%5E%7B%5Cfrac%7B1%7D%7B4%7D%2A4%20%7D%20%3D16%2A7%3D%20112)
2)![\displaystyle \sqrt[4]{8}*\sqrt[4]{1250}=\sqrt[4]{8*1250} =\sqrt[4]{16*625} =\sqrt[4]{2^{4}*5^{4}} =2*5=10 \displaystyle \sqrt[4]{8}*\sqrt[4]{1250}=\sqrt[4]{8*1250} =\sqrt[4]{16*625} =\sqrt[4]{2^{4}*5^{4}} =2*5=10](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B4%5D%7B8%7D%2A%5Csqrt%5B4%5D%7B1250%7D%3D%5Csqrt%5B4%5D%7B8%2A1250%7D%20%20%20%3D%5Csqrt%5B4%5D%7B16%2A625%7D%20%20%3D%5Csqrt%5B4%5D%7B2%5E%7B4%7D%2A5%5E%7B4%7D%7D%20%3D2%2A5%3D10)
3)![\displaystyle \sqrt[5]{-7}*\sqrt[5]{49} *\sqrt[5]{49} =\sqrt[5]{(-7)*7^{2}*7^{2}} =\sqrt[5]{(-7)^{5}} =-7 \displaystyle \sqrt[5]{-7}*\sqrt[5]{49} *\sqrt[5]{49} =\sqrt[5]{(-7)*7^{2}*7^{2}} =\sqrt[5]{(-7)^{5}} =-7](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B5%5D%7B-7%7D%2A%5Csqrt%5B5%5D%7B49%7D%20%2A%5Csqrt%5B5%5D%7B49%7D%20%3D%5Csqrt%5B5%5D%7B%28-7%29%2A7%5E%7B2%7D%2A7%5E%7B2%7D%7D%20%3D%5Csqrt%5B5%5D%7B%28-7%29%5E%7B5%7D%7D%20%3D-7)
4)
5)![\displaystyle 0,2*\sqrt[5]{-32}+\sqrt[4]{81}-\sqrt[6]{1}= 0,2*\sqrt[5]{(-2)^{5}}+\sqrt[4]{3^{4}}-\sqrt[6]{1^{6}}=0,2*(-2)+3-1=-0,4+2=1,6 \displaystyle 0,2*\sqrt[5]{-32}+\sqrt[4]{81}-\sqrt[6]{1}= 0,2*\sqrt[5]{(-2)^{5}}+\sqrt[4]{3^{4}}-\sqrt[6]{1^{6}}=0,2*(-2)+3-1=-0,4+2=1,6](https://tex.z-dn.net/?f=%5Cdisplaystyle%200%2C2%2A%5Csqrt%5B5%5D%7B-32%7D%2B%5Csqrt%5B4%5D%7B81%7D-%5Csqrt%5B6%5D%7B1%7D%3D%20%20%200%2C2%2A%5Csqrt%5B5%5D%7B%28-2%29%5E%7B5%7D%7D%2B%5Csqrt%5B4%5D%7B3%5E%7B4%7D%7D-%5Csqrt%5B6%5D%7B1%5E%7B6%7D%7D%3D0%2C2%2A%28-2%29%2B3-1%3D-0%2C4%2B2%3D1%2C6)
6)![\displaystyle \sqrt[5]{2-\sqrt{5} } *\sqrt[5]{2+\sqrt{5} }=\sqrt[5]{(2-\sqrt{5})(2+\sqrt{5}) }=\sqrt[5]{2^{2}-(\sqrt{5})^{2} }=\sqrt[5]{4-5}=\sqrt[5]{-1} =-1 \displaystyle \sqrt[5]{2-\sqrt{5} } *\sqrt[5]{2+\sqrt{5} }=\sqrt[5]{(2-\sqrt{5})(2+\sqrt{5}) }=\sqrt[5]{2^{2}-(\sqrt{5})^{2} }=\sqrt[5]{4-5}=\sqrt[5]{-1} =-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B5%5D%7B2-%5Csqrt%7B5%7D%20%7D%20%2A%5Csqrt%5B5%5D%7B2%2B%5Csqrt%7B5%7D%20%7D%3D%5Csqrt%5B5%5D%7B%282-%5Csqrt%7B5%7D%29%282%2B%5Csqrt%7B5%7D%29%20%20%7D%3D%5Csqrt%5B5%5D%7B2%5E%7B2%7D-%28%5Csqrt%7B5%7D%29%5E%7B2%7D%20%7D%3D%5Csqrt%5B5%5D%7B4-5%7D%3D%5Csqrt%5B5%5D%7B-1%7D%20%3D-1)