Question

Освободитесь от иррациональности в знаменателе дроби:

Answer 1

$\frac{5}{\sqrt{10}}=\frac{5\sqrt{10}}{10}=\frac{\sqrt{10}}{2}\\\\\frac{30}{\sqrt{15}}=\frac{30\sqrt{15}}{15}=2\sqrt{15}\\\\\frac{7+\sqrt8}{\sqrt8-5}=\frac{(7+\sqrt8)(\sqrt8+5)}{(\sqrt8-5)(\sqrt8+5)}=\frac{7\sqrt8+35+8+5\sqrt8}{8-25}=-\frac{43+12\sqrt8}{17}$

Answer 2

5/√10 = 5√10/10 = √10/2

30/√15 = 30√15/15 = 2√15

(7+√8)/(√8-5) = (7+√8)(√8+5) / (√8-5)(√8+5) =

= (7√8+8+5√8+35)/(8-25) = -(43+12√8)/17