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
