Question

doprowadz wyrazenie do najprostrzej postaci;

√75-√27+√12=

(2√2+3)²=

(1+√7)(1-√7)=

√72+√32-√8=

(3√3-2)²=

(2+√5)(2-√5)=

oblicz:

5×(2½)⁻¹=

√5 i 9/27÷√1 i 3/9=

∛4×∛250-√7×√63=

(1⅓)⁻¹÷2=

(√54÷√3)÷√2=

√15×√⅗+∛20×∛⅖=

Answer 1

√75-√27+√12 = √(25·3)-√(9·3)+√(4·3) = √25√3-√9·√3+√4·√3 = 5√3-3√3+2√3 = 4√3

(2√2+3)² = (2√2)²+2·2√2·3+3² = 8+12√2+9 = 17+12√2

(1+√7)(1-√7) = 1²-(√7)² = 1-7 = -6

√72+√32-√8 = √(36·2)+√(16·2)-√(4·2) = 6√2+4√2-2√2 = 8√2 

(3√3-2)² = (3√3)²-2·3√3·2+2² = 27-12√3+4 = 31-12√3

(2+√5)(2-√5) = 2²-(√5)² = 4-5 = -1

 

5·(2½)⁻¹ = 5·(5/2)⁻¹ = 5·(2/5) = 2

⁹/₂₇√5 : ³/₉√1 = ⅓√5 : ⅓√1 = √(5/1) = √5 

∛4·∛250-√7·√63 = ∛(4·250)-√(7·63) = ∛1000-√441 = 10-21 = -11

(1⅓)⁻¹ : 2 = (4/3)⁻¹ : 2 = ¾ :2 = 3/8

(√54 : √3) : √2 = √(54/3) : √2 = √18 : √2 = √(18/2) = √9 = 3

√15·√⅗ + ∛20·∛⅖ = √(15·⅗)+∛(20·⅖) = √9+∛8 = 3+2 = 5