Đáp án:

Giải thích các bước giải:

1)$\frac{15}{√5}$ =$\frac{3×5}{√5}$ 

=3√5

2)$\frac{3}{√2}$ =$\frac{3×√2}{√2×√2}$ 

=$\frac{3√2}{2}$ 

3)$\frac{-10}{√2}$ =$\frac{-5×2}{√2}$ 

=-5√2

4)$\frac{5-√5}{√5-1}$ 

=$\frac{(5-√5)×(√5+1)}{(√5-1)×(√5+1)}$ 

=$\frac{5√5+5-5-√5}{5-1}$ 

=$\frac{4√5}{4}$=√5

=$\frac{3√5}{2}$ 

5)$\frac{2√3-3√2}{√2-√3}$ 

=$\frac{(2√3-3√2)×(√2+√3)}{(√2-√3)×(√2+√3)}$ 

=$\frac{2√6+6-6-3√6}{2-3}$ 

=$\frac{-√6}{-1}$ =√6

6)$\frac{√6-√2}{√3+1}$ 

=$\frac{(√6-√2)×(√3-1)}{(√3+1)×(√3-1)}$ 

=$\frac{3√2-√6-√6+√2}{3-1}$ 

=$\frac{4√2-2√6}{2}$ 

=$\frac{2(2√2-√6}{2}$=2√2-√6

7)$\frac{2√3-√6}{√2-1}$ 

=$\frac{(2√3-√6)×(√2+1)}{(√2-1)×(√2+1)}$ 

=$\frac{2√6+2√3-2√3-√6}{2-1}$ 

=√6

8)$\frac{12}{√5-1}$ 

=$\frac{12(√5+1)}{(√5-1)×(√5+1)}$

=$\frac{12(√5+1)}{5-1}$

=$\frac{12(√5+1)}{4}$

=3√5+3

9)$\frac{15}{√5+2}$ 

 =$\frac{15(√5-2}{(√5+2)×(√5-2)}$ 

=$\frac{15(√5-2}{5-4}$ 

=$\frac{15(√5-2}{1}$

=15√5-30

10)$\frac{12}{√7-2}$  

=$\frac{12(√7+2)}{(√7-2)×(√7+2)}$  

=$\frac{12(√7+2)}{7-4}$ 

=$\frac{12(√7+2)}{3}$

=4√7+8

11)$\frac{10}{√10-2}$ =$\frac{10(√10+2)}{(√10-2)×(√10+2)}$

=$\frac{10(√10+2)}{10-4}$

=$\frac{10(√10+2)}{6}$

=$\frac{5(√10+2)}{3}$

=$\frac{5√10+10)}{3}$

12)$\frac{9}{√5-√2}$ 

=$\frac{9(√5+√2)}{(√5-√2)×(√5+√2)}$ 

=$\frac{9(√5+√2)}{5-2}$ 

=$\frac{9(√5+√2)}{3}$

=3√5-3√2

13)$\frac{-5}{√7-√2}$  

=$\frac{-5(√7+√2)}{(√7-√2)×(√7+√2)}$ 

=$\frac{-5(√7+√2)}{7-2}$ 

=$\frac{-5(√7+√2)}{5}$

=-√7-√2

14)$\frac{12}{3√2-2√3}$  

=$\frac{12(3√2+2√3)}{(3√2-2√3)×(3√2+2√3)}$ 

=$\frac{12(3√2+2√3)}{18-12}$ 

=$\frac{12(3√2+2√3)}{6}$ 

=6√2+4√3

15)$\frac{12}{2-√7}$ 

=$\frac{12(2+√7)}{(2-√7)×(2+√7)}$ 

=$\frac{12(2+√7)}{4-7}$ 

=$\frac{12(2+√7)}{-3}$ 

=-8-4√7