1. а) 7 и √48
√49 и √48
49 > 48 ⇒ √49 > √48 ⇒ 7 > √48
б) 2√3 и 3√2
√4√3 и √9√2
√12 и √18
12 < 18 ⇒ √12 < √18 ⇒ 2√3 < 3√2
2. √81*49 = √81 * √49 = 9 * 7 = 63
√ 0,3*120 = √36 = 6
√125 / √5 = √5*25 / √5 = √5*√25 / √5 = 5√5 / √5 = 5/1 = 5
√2 1/4 = √(9/4) = √9 / √4 = 3/2 = 1,5
√(-17)² = 17
√3⁶ = √(3³)² = 3³ = 27
3. а) 3√8 + √2 - 3√18 = 3√4*2 + √2 - 3√9*2 = 3*2*√2 + √2 - 3*3√2 =
= 6√2 + √2 - 9√2 = - 2√2
б) (√5 - √2)² = (√5 )² - 2*√5*√2 + (√2 )² = 5 - 2√10 + 2 = 7 - 2√10
в) (2 - √3)(2 + √3) = 2² - √3² = 4 - 3 = 1
4 √8а³ = √2*4*а²а = √2*√4*√а²√а = 2а√2а
5 (х² - 3) / (х + √3) = (х +√3) (х-√3) / (х +√3) = (х-√3) / 1 = х-√3
(√х + √y) / х - y = (√х + √y ) / (√х - + √y ) (√х + √y ) =
= 1 / (√х - + √y )
6. 5/√7 = 5√7 /√7√7 = 5√7 / 7
1 / (2+√3) = 1*(2-√3) / (2+√3)(2-√3) = (2-√3) / (2² - √3²) = (2-√3) / (4 - 3) =
= (2-√3) / 1 = 2-√3