1)
![\displaystyle \sqrt{6^4} = \sqrt{(6^2)^2}=6^2=36](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B6%5E4%7D%20%3D%20%5Csqrt%7B%286%5E2%29%5E2%7D%3D6%5E2%3D36%20)
2)
![\displaystyle \sqrt{(-5)^6}= \sqrt{(-1)^6*5^6}= \sqrt{1*(5^3)^2}=5^3=125](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-5%29%5E6%7D%3D%20%5Csqrt%7B%28-1%29%5E6%2A5%5E6%7D%3D%20%5Csqrt%7B1%2A%285%5E3%29%5E2%7D%3D5%5E3%3D125%20)
Заметим что Четная степень отрицательного числа = положительному числу
3)
![\displaystyle \sqrt{(-8)^4}= \sqrt{(-1)^4*8^4}=8^2=64](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-8%29%5E4%7D%3D%20%5Csqrt%7B%28-1%29%5E4%2A8%5E4%7D%3D8%5E2%3D64%20%20)
4)
![\displaystyle \sqrt{0.1^6}= \sqrt{(0.1^3)^2}=0.1^3= 0.001](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B0.1%5E6%7D%3D%20%5Csqrt%7B%280.1%5E3%29%5E2%7D%3D0.1%5E3%3D%200.001)
5)
![\displaystyle \sqrt{(-1)^{4n}}= \sqrt{((-1)^2)^{2n}} =\sqrt{1^{2n}}= 1^{2n}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-1%29%5E%7B4n%7D%7D%3D%20%5Csqrt%7B%28%28-1%29%5E2%29%5E%7B2n%7D%7D%20%3D%5Csqrt%7B1%5E%7B2n%7D%7D%3D%201%5E%7B2n%7D%3D1%20)
6)
![\displaystyle \sqrt{(-1)^{4n+6}}= \sqrt{((-1)^2)^{2n+3}}= \sqrt{1^{2n+3}}=1^{2n+3}=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Csqrt%7B%28-1%29%5E%7B4n%2B6%7D%7D%3D%20%5Csqrt%7B%28%28-1%29%5E2%29%5E%7B2n%2B3%7D%7D%3D%20%5Csqrt%7B1%5E%7B2n%2B3%7D%7D%3D1%5E%7B2n%2B3%7D%3D1%20%20%20)
Длина единичной окружности: с= 2·π·1 = 2π.
4.2
Дуга АМ =
![\frac{c}{8}=\frac{2 \pi }{8}=\frac{\pi }{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B8%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B%5Cpi+%7D%7B4%7D)
Дуга BD =
![\frac{c}{2}=\frac{2 \pi }{2}=\pi](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B2%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B2%7D%3D%5Cpi)
Дуга CK =
![c*\frac{10}{12}=\frac{5c}{6}=\frac{5*2 \pi }{6}=\frac{5\pi }{3}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B10%7D%7B12%7D%3D%5Cfrac%7B5c%7D%7B6%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B6%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B3%7D)
Дуга MP =
![c*(\frac{1}{8}+\frac{2}{12})=c*(\frac{1}{8}+\frac{1}{6})=\frac{7c}{24}=\frac{7*2 \pi }{24}=\frac{7\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B2%7D%7B12%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B6%7D%29%3D%5Cfrac%7B7c%7D%7B24%7D%3D%5Cfrac%7B7%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B12%7D)
Дуга DM =
![c*\frac{3}{8}=\frac{3*2 \pi }{8}=\frac{3\pi }{4}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B3%7D%7B8%7D%3D%5Cfrac%7B3%2A2+%5Cpi+%7D%7B8%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B4%7D)
Дуга MK =
![c*(\frac{1}{8}+\frac{1}{12})=\frac{5c}{24}=\frac{5*2 \pi }{24}=\frac{5\pi }{12}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B8%7D%2B%5Cfrac%7B1%7D%7B12%7D%29%3D%5Cfrac%7B5c%7D%7B24%7D%3D%5Cfrac%7B5%2A2+%5Cpi+%7D%7B24%7D%3D%5Cfrac%7B5%5Cpi+%7D%7B12%7D)
Дуга CP =
![c*\frac{11}{12}=\frac{11*2 \pi }{12}=\frac{11\pi }{6}](https://tex.z-dn.net/?f=c%2A%5Cfrac%7B11%7D%7B12%7D%3D%5Cfrac%7B11%2A2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B11%5Cpi+%7D%7B6%7D)
Дуга PC =
![\frac{c}{12}=\frac{2 \pi }{12}=\frac{\pi }{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7B12%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B12%7D%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D)
4.3
Дуга АМ =
![\frac{2}{5}*\frac{c}{4}=\frac{c}{10}=\frac{2 \pi }{10}=\frac{\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7Bc%7D%7B10%7D%3D%5Cfrac%7B2+%5Cpi+%7D%7B10%7D%3D%5Cfrac%7B%5Cpi+%7D%7B5%7D)
Дуга МB =
![\frac{3}{5}*\frac{c}{4}=\frac{3c}{20}=\frac{3*2\pi }{20}=\frac{3\pi }{10}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7Bc%7D%7B4%7D%3D%5Cfrac%7B3c%7D%7B20%7D%3D%5Cfrac%7B3%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B3%5Cpi+%7D%7B10%7D)
Дуга DМ =
![c*(\frac{1}{4}+\frac{2}{5}*\frac{1}{4})=c*(\frac{1}{4}+\frac{1}{10})=\frac{7c}{20}=\frac{7*2\pi }{20}=\frac{7\pi }{10}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B2%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B10%7D%29%3D%5Cfrac%7B7c%7D%7B20%7D%3D%5Cfrac%7B7%2A2%5Cpi+%7D%7B20%7D%3D%5Cfrac%7B7%5Cpi+%7D%7B10%7D)
Дуга МC =
![c*(\frac{3}{5}*\frac{1}{4}+\frac{1}{4})=c*(\frac{3}{20}+\frac{1}{4})=\frac{8c}{20}=\frac{2c}{5}=\frac{2*2\pi }{5}=\frac{4\pi }{5}](https://tex.z-dn.net/?f=c%2A%28%5Cfrac%7B3%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3Dc%2A%28%5Cfrac%7B3%7D%7B20%7D%2B%5Cfrac%7B1%7D%7B4%7D%29%3D%5Cfrac%7B8c%7D%7B20%7D%3D%5Cfrac%7B2c%7D%7B5%7D%3D%5Cfrac%7B2%2A2%5Cpi+%7D%7B5%7D%3D%5Cfrac%7B4%5Cpi+%7D%7B5%7D)
Х²-5х-6=0
По теореме Виета
{х1+х2=5
{х1*х2=-6
{х1=6
{х2=-1
1) 92*40=3680- метров отремонтиролвала 1 бригада
2) 95*48=4560- метров отремонтировала 2 бригада
3)9700-3680-4560=1460 - метров отрементировала 3 бригада
![2 \sqrt{10}= \sqrt{2^2*10}= \sqrt{4*10}= \sqrt{40} \\\\6,5= \sqrt{6,5^2}= \sqrt{42,25} \\\\ \sqrt{41} \\\\ \sqrt{42,25} > \sqrt{41}> \sqrt{40} \\\\6,5> \sqrt{41}> 2\sqrt{10}](https://tex.z-dn.net/?f=2+%5Csqrt%7B10%7D%3D+%5Csqrt%7B2%5E2%2A10%7D%3D+%5Csqrt%7B4%2A10%7D%3D+%5Csqrt%7B40%7D++%5C%5C%5C%5C6%2C5%3D+%5Csqrt%7B6%2C5%5E2%7D%3D+%5Csqrt%7B42%2C25%7D+%5C%5C%5C%5C+%5Csqrt%7B41%7D+%5C%5C%5C%5C+%5Csqrt%7B42%2C25%7D+%3E+%5Csqrt%7B41%7D%3E+%5Csqrt%7B40%7D+%5C%5C%5C%5C6%2C5%3E+%5Csqrt%7B41%7D%3E+2%5Csqrt%7B10%7D++++++)
Ответ: 6,5; <span>√41; </span><span>2<span>√10</span></span>