7. a) 4,6 и √22 б) 2√37 и 5√6
√4,6² и √22 √4*37 и √25*6
√21,16 и √22 √148 и √150
√21,16 < √22 √148 < √150<br> 4.6 <√22 2√37 < 5√6<br>
8. а) (5√3 - √15) / √5 - 1 = [(5√3 - √15) / (√5 - 1)] * [(√5 +1)/(√5 + 1)]=
=(5√15 - √75 +5√3 - √15) / (5-1)=
=(5√15 - √15 + 5√3 - 5√3) / 4= (4√15) / 4=√15
б) (√27 + √12 + 5) (1-√3)=
=√27 + √12 + 5 - √27*3 - √12*3 - 5√3 =
=√9*3 + √4*3 + 5 - √81 - √36 - 5√3 =
=3√3 + 2√3 + 5 - 9 - 6 - 5√3 =
=5√3 - 5√3 - 10= - 10
в) (2√6 - 3√3) / (1 - √2)² = (2√3 * √2 - 3√3) / (1 - 2√2 +2)=
=(√3 (2√2 - 3)) / (3 - 2√2) = -(√3 (3 - 2√2)) / (3 - 2√2)= -√3
г) (√4(х-у)²) / (х-у)=
=(4(х-у)) / (х-у) =
=4
9. ху²√х/у³ = √х²ху⁴/у³ = √х³у
10. 1-2√х+х = - (1-√х)² = - (1-√х)(1-√х) = -(1-√х)(1-√х) =- (1-√х)
х-1 1-х 1²-(√х)² (1-√х)(1+√х) 1+√х
=√х - 1
1+√х
11. √2+1 = √2+1 * √2+1 = (√2+1)² =2+2√2+1 = 3+2√2
√2-1 √2-1 √2+1 2-1 1