I вариант:
1. а) ![\sqrt{144} + 5\sqrt{0,64} = 12 + 16 = 28 \sqrt{144} + 5\sqrt{0,64} = 12 + 16 = 28](https://tex.z-dn.net/?f=%5Csqrt%7B144%7D%20%2B%205%5Csqrt%7B0%2C64%7D%20%3D%2012%20%2B%2016%20%3D%2028)
б) ![(4\sqrt{2})^2 = 32^2 = 1024 (4\sqrt{2})^2 = 32^2 = 1024](https://tex.z-dn.net/?f=%284%5Csqrt%7B2%7D%29%5E2%20%3D%2032%5E2%20%3D%201024)
в) ![\sqrt{0,16*25} - 6 \sqrt{\frac{1}{36} } = 2 - 6*\frac{1}{6} = 2 - 0,96 = 1,04 \sqrt{0,16*25} - 6 \sqrt{\frac{1}{36} } = 2 - 6*\frac{1}{6} = 2 - 0,96 = 1,04](https://tex.z-dn.net/?f=%5Csqrt%7B0%2C16%2A25%7D%20-%206%20%5Csqrt%7B%5Cfrac%7B1%7D%7B36%7D%20%7D%20%3D%202%20-%206%2A%5Cfrac%7B1%7D%7B6%7D%20%3D%202%20-%200%2C96%20%3D%201%2C04)
2. а) ![\sqrt{11} * \sqrt{44} = \sqrt{484} = 22 \sqrt{11} * \sqrt{44} = \sqrt{484} = 22](https://tex.z-dn.net/?f=%5Csqrt%7B11%7D%20%2A%20%5Csqrt%7B44%7D%20%3D%20%5Csqrt%7B484%7D%20%3D%2022)
б) ![\frac{\sqrt{44} }{\sqrt{11} } = \sqrt{4} = 2 \frac{\sqrt{44} }{\sqrt{11} } = \sqrt{4} = 2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B44%7D%20%7D%7B%5Csqrt%7B11%7D%20%7D%20%3D%20%5Csqrt%7B4%7D%20%3D%202)
в) ![\sqrt{6^4} = \sqrt{1296} = 36 \sqrt{6^4} = \sqrt{1296} = 36](https://tex.z-dn.net/?f=%5Csqrt%7B6%5E4%7D%20%3D%20%5Csqrt%7B1296%7D%20%3D%2036)
3. а) ![\sqrt{x} = 3 \sqrt{x} = 3](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%203)
![\sqrt{x^2} = 3^2 \sqrt{x^2} = 3^2](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%20%3D%203%5E2)
x = 9
б) x² = 3
x²-3 = 0
x = ±√3
в) x² = -3
x²+3 = 0
x = ±√3
г) x²-2,25 = 0
x = ±√2,25
x = ±15
II вариант:
1. а) 4√0,81 + √196 = 4*4*0,81 + 14 = 12,96 + 14 = 26,96
б) ![(3\sqrt{7})^2 = 3*3*7 = 63^2 = 3969 (3\sqrt{7})^2 = 3*3*7 = 63^2 = 3969](https://tex.z-dn.net/?f=%283%5Csqrt%7B7%7D%29%5E2%20%3D%203%2A3%2A7%20%3D%2063%5E2%20%3D%203969)
в) ![\sqrt{0,04*81} - 7\sqrt{\frac{1}{49} } = 1,8 - 0,98 = 0,82 \sqrt{0,04*81} - 7\sqrt{\frac{1}{49} } = 1,8 - 0,98 = 0,82](https://tex.z-dn.net/?f=%5Csqrt%7B0%2C04%2A81%7D%20-%207%5Csqrt%7B%5Cfrac%7B1%7D%7B49%7D%20%7D%20%3D%201%2C8%20-%200%2C98%20%3D%200%2C82)
2. а) √7 * √28 = √196 = 14
б) ![\frac{\sqrt{28} }{\sqrt{7} } = \sqrt{4} = 2 \frac{\sqrt{28} }{\sqrt{7} } = \sqrt{4} = 2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B28%7D%20%7D%7B%5Csqrt%7B7%7D%20%7D%20%3D%20%20%5Csqrt%7B4%7D%20%3D%202)
в) ![\sqrt{3^6} = \sqrt{729} = 27 \sqrt{3^6} = \sqrt{729} = 27](https://tex.z-dn.net/?f=%5Csqrt%7B3%5E6%7D%20%3D%20%5Csqrt%7B729%7D%20%3D%2027)
3. а) ![\sqrt{x} = 6 \sqrt{x} = 6](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%3D%206)
x² = 6²
x = 36
б) x² = 6
x²-6 = 0
x = ±√6
в) x² = -6
x²+6 = 0
x = ±√6
г) x²-1,21 = 0
x = ±√1,21
x = ±1,1