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1)(7√3 +14√48-√147):2√3 = (7√3+56√3-7√3):2√3=56√3:2√3=28
2)(√3 + 5)(√3 - 5) = 3-25= -22
3)(√2+√5)(√2-√5) = 2-5 = -3
4)(√2+1)² = 2+2√2+1 = 3+2√2
5)
(2√(2/3) - 8√(3/8) + 4√(2/3)): √(2/3) = (6√(2/3) - 8√(3/8)): √(2/3) =
6√(2/3)-8√(3/8) 6√(2/3)-8√(3/8) (6√(2/3)-8√(3/8))√3
= ---------------------- = --------------------- = ---------------------------- =
√(2/3) √2/√3 √2
6√(6/3)-8√(9/8) 6√2 - 8 3/√8 6√2 - 6√2
= ---------------------- = ------------------ = ---------------- = 0
√2 √2 √2
6) 2√20 + 1,5√28 +√45 - √63 = 4√5 + 3√7 + 3√5 - 3√7 = 4√5 +3√5 = 7√5
7)(√7-1)(√7+1) = 7-1 = 6
8)(√5-3)² = 5 - 6√5 + 9 = 14-6√5
9)(√5+√7)² = 5 + 2√35 + 7 = 12 + 2√35
10)(√5-√3)² = 5 - 2√15 + 3 = 8 - 2√15
11) 5 7 5 + 21 26 4
10 ---- + 2 ----- = 12 --------------- = 12 ------- = 13 -----
6 18 18 18 9
12) 13,7 - 18, 85 = -5,15
13) 12 3 12 * 34 * 1
------ : ------ *(-0,25) = ----------------- = 2
17 34 17 * 3 * 4
14)|-4,5| + |3,6| = 8,1
15) 7 2 1
21,7 : ( 3 ---- - 1-----) = 21,7 : 2---- ≈ 21,7 : 2,3 ≈ 9,435
15 15 3
16) 1,27 * 10⁻³ < 5,41 * 10⁻⁴
127 * 10⁻⁵ < 541 * 10⁻⁶
17) √125 * √20 √2500 2
√(125/3) : √(3/20) = ---------------- = ---------- = 50/3 = 16 ----
√3 * √3 3 3
3 5 3(√3 - √2) + 5(√3 + √2)
18) ------------- + ------------ = ---------------------------------- =
√3 + √2 √3 - √2 (√3 + √2)(√3 - √2)
3√3 - 3√2 +5√3 + 5√2 8√3 + 2√2 8√3 + 2√2
= -------------------------------- = --------------------------- = ------------------- =
(√3 + √2)(√3 - √2) (√3 + √2)(√3 - √2) 1
= 8√3 + 2√2
11 5 11 - 10 1
19) 5----- - 3---- = 2 ----------- = 2-----
12 6 12 12
20) -21,35 + (-15,65) = -37
2)(√3 + 5)(√3 - 5) = 3-25= -22
3)(√2+√5)(√2-√5) = 2-5 = -3
4)(√2+1)² = 2+2√2+1 = 3+2√2
5)
(2√(2/3) - 8√(3/8) + 4√(2/3)): √(2/3) = (6√(2/3) - 8√(3/8)): √(2/3) =
6√(2/3)-8√(3/8) 6√(2/3)-8√(3/8) (6√(2/3)-8√(3/8))√3
= ---------------------- = --------------------- = ---------------------------- =
√(2/3) √2/√3 √2
6√(6/3)-8√(9/8) 6√2 - 8 3/√8 6√2 - 6√2
= ---------------------- = ------------------ = ---------------- = 0
√2 √2 √2
6) 2√20 + 1,5√28 +√45 - √63 = 4√5 + 3√7 + 3√5 - 3√7 = 4√5 +3√5 = 7√5
7)(√7-1)(√7+1) = 7-1 = 6
8)(√5-3)² = 5 - 6√5 + 9 = 14-6√5
9)(√5+√7)² = 5 + 2√35 + 7 = 12 + 2√35
10)(√5-√3)² = 5 - 2√15 + 3 = 8 - 2√15
11) 5 7 5 + 21 26 4
10 ---- + 2 ----- = 12 --------------- = 12 ------- = 13 -----
6 18 18 18 9
12) 13,7 - 18, 85 = -5,15
13) 12 3 12 * 34 * 1
------ : ------ *(-0,25) = ----------------- = 2
17 34 17 * 3 * 4
14)|-4,5| + |3,6| = 8,1
15) 7 2 1
21,7 : ( 3 ---- - 1-----) = 21,7 : 2---- ≈ 21,7 : 2,3 ≈ 9,435
15 15 3
16) 1,27 * 10⁻³ < 5,41 * 10⁻⁴
127 * 10⁻⁵ < 541 * 10⁻⁶
17) √125 * √20 √2500 2
√(125/3) : √(3/20) = ---------------- = ---------- = 50/3 = 16 ----
√3 * √3 3 3
3 5 3(√3 - √2) + 5(√3 + √2)
18) ------------- + ------------ = ---------------------------------- =
√3 + √2 √3 - √2 (√3 + √2)(√3 - √2)
3√3 - 3√2 +5√3 + 5√2 8√3 + 2√2 8√3 + 2√2
= -------------------------------- = --------------------------- = ------------------- =
(√3 + √2)(√3 - √2) (√3 + √2)(√3 - √2) 1
= 8√3 + 2√2
11 5 11 - 10 1
19) 5----- - 3---- = 2 ----------- = 2-----
12 6 12 12
20) -21,35 + (-15,65) = -37
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