№8
1) ![\sqrt{7y^2}=\sqrt{7*y^2}=\sqrt{7}*\sqrt{y^2}=\sqrt{7}*|y|=-y\sqrt{7} \sqrt{7y^2}=\sqrt{7*y^2}=\sqrt{7}*\sqrt{y^2}=\sqrt{7}*|y|=-y\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B7y%5E2%7D%3D%5Csqrt%7B7%2Ay%5E2%7D%3D%5Csqrt%7B7%7D%2A%5Csqrt%7By%5E2%7D%3D%5Csqrt%7B7%7D%2A%7Cy%7C%3D-y%5Csqrt%7B7%7D)
2) ![\sqrt{32a^8}=\sqrt{16a^8*2}=\sqrt{16a^8}*\sqrt{2}=4a^4\sqrt{2} \sqrt{32a^8}=\sqrt{16a^8*2}=\sqrt{16a^8}*\sqrt{2}=4a^4\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B32a%5E8%7D%3D%5Csqrt%7B16a%5E8%2A2%7D%3D%5Csqrt%7B16a%5E8%7D%2A%5Csqrt%7B2%7D%3D4a%5E4%5Csqrt%7B2%7D)
3) ![\sqrt{-b^{15}}=\sqrt{b^{14}*(-b)}=\sqrt{b^{14}}*\sqrt{-b}=|b^7|\sqrt{-b}=-b^7\sqrt{-b} \sqrt{-b^{15}}=\sqrt{b^{14}*(-b)}=\sqrt{b^{14}}*\sqrt{-b}=|b^7|\sqrt{-b}=-b^7\sqrt{-b}](https://tex.z-dn.net/?f=%5Csqrt%7B-b%5E%7B15%7D%7D%3D%5Csqrt%7Bb%5E%7B14%7D%2A%28-b%29%7D%3D%5Csqrt%7Bb%5E%7B14%7D%7D%2A%5Csqrt%7B-b%7D%3D%7Cb%5E7%7C%5Csqrt%7B-b%7D%3D-b%5E7%5Csqrt%7B-b%7D)
4) ![\sqrt{-x^{14}y^3}=\sqrt{x^{14}y^2*(-y)}=\sqrt{x^{14}y^2}*\sqrt{-y}=|x^7y|\sqrt{-y}=-x^7y\sqrt{-y} \sqrt{-x^{14}y^3}=\sqrt{x^{14}y^2*(-y)}=\sqrt{x^{14}y^2}*\sqrt{-y}=|x^7y|\sqrt{-y}=-x^7y\sqrt{-y}](https://tex.z-dn.net/?f=%5Csqrt%7B-x%5E%7B14%7Dy%5E3%7D%3D%5Csqrt%7Bx%5E%7B14%7Dy%5E2%2A%28-y%29%7D%3D%5Csqrt%7Bx%5E%7B14%7Dy%5E2%7D%2A%5Csqrt%7B-y%7D%3D%7Cx%5E7y%7C%5Csqrt%7B-y%7D%3D-x%5E7y%5Csqrt%7B-y%7D)
№9
![\sqrt{(5-\sqrt{12})^2}+\sqrt{(3-\sqrt{12})^2}=|5-\sqrt{12}|+|3-\sqrt{12}|=(5-\sqrt{12})+(\sqrt{12}-3)=5-3=2 \sqrt{(5-\sqrt{12})^2}+\sqrt{(3-\sqrt{12})^2}=|5-\sqrt{12}|+|3-\sqrt{12}|=(5-\sqrt{12})+(\sqrt{12}-3)=5-3=2](https://tex.z-dn.net/?f=%5Csqrt%7B%285-%5Csqrt%7B12%7D%29%5E2%7D%2B%5Csqrt%7B%283-%5Csqrt%7B12%7D%29%5E2%7D%3D%7C5-%5Csqrt%7B12%7D%7C%2B%7C3-%5Csqrt%7B12%7D%7C%3D%285-%5Csqrt%7B12%7D%29%2B%28%5Csqrt%7B12%7D-3%29%3D5-3%3D2)
Первый модуль раскрывается без изменений, а во втором знак меняется на противоположный, поскольку
12\\\sqrt{25}>\sqrt{12}\\5>\sqrt{12}\\5-\sqrt{12}>0\\|5-\sqrt{12}|=5-\sqrt{12}\\\\9<12\\\sqrt{9}<\sqrt{12}\\3<\sqrt{12}\\3-\sqrt{12}<0\\|3-\sqrt{12}|=-(3-\sqrt{12})=\sqrt{12}-3" alt="25>12\\\sqrt{25}>\sqrt{12}\\5>\sqrt{12}\\5-\sqrt{12}>0\\|5-\sqrt{12}|=5-\sqrt{12}\\\\9<12\\\sqrt{9}<\sqrt{12}\\3<\sqrt{12}\\3-\sqrt{12}<0\\|3-\sqrt{12}|=-(3-\sqrt{12})=\sqrt{12}-3" align="absmiddle" class="latex-formula">