1.
а) 1/6 * √144 + 1/3 * √0.81 = 1/6 * 12 + 1/3 * 9/10 = 2 + 3/10 = 2 3/10 = 2.3
б) 2.1 + 1.3 * √81/169 = 2.1 + 1.3 * 9/13 = 2 1/10 + 1 3/10 * 9/13 =
21/10 + 117/130 = 273/130 + 117/130 = 390/130 = 3
в) (0.4 √5)^2 = √(0.16 * 5)^2 = √0.8 ^2 = 0.8
г) √(225 * 0.04) = √9 = 3
д) √28 * √63 = √1764 = 42
е) √48 / √3 = 4√3 / √3 = 4
ж) √(2^6 * 7^2) = √64 * 49 = √3136 = 56
2.
a) 2√2 + √50 - √98 = 2√2 + 5√2 - 7√2 = 0
б) (3√5 - √20) * √5 = (3√5 - 2√5) * √5 = √5 * √5 = 5
в) (2 - √3)(2+√3) = 2^2 - √3^2 = 2 - 3 = -1
г) (√3 + √2)^2 = 3 + 2√6 + 2 = 5 + 2√6
3.
а) 2 / 3√7 = (2 * √7) / (3 * √7 * √7) = 2√7 / 21
б) 4 / (√11 + 3) = 4(√11 + 3) / (√11 + 3)(√11 + 3) =
4√11 + 12 / 11 + 3 = 4√11 + 12 / 14 = (4√11 + 6) / 7
5.
1 / (1 - 3√5) + 1/(1 + 3√5) = (1 + 3√5 + 1 - 3√5) / (1 - 3√5)(1 + 3√5) =
2 / 1 + 3√5 - 3√5 - 45 = 2 / (-44) = -1 / 22
6.
а) x^2 = 0.81
x = ±0.9
б) x^2 = 46
x = √46
в) |x - 5| = 1
(x - 5)^2 = 1
x^2 - 10x + 25 = 1
x^2 - 10x + 24 = 0
D = 100 - 4 * 1 * 24 = 4
x1 = 10 + 2 / 2 = 6
x2 = 10 - 2 / 2 = 4
г) |x + 3| = 2
(x + 3)^2 = 4
x^2 + 6x + 9 = 4
x^2 + 6x + 5 = 0
D = 36 - 4 * 1 * 5 = 16
x1 = (-6) + 4 / 2 = -1
x2 = (-6) - 4 / 2 = -5