1 bài tập Trục căn ở mẫu (có lời giải)

a) $\frac{5}{{\sqrt {10} }} = \frac{{5\sqrt {10} }}{{10}} = \frac{{\sqrt {10} }}{2};$ $\frac{5}{{2\sqrt 5 }} = \frac{{{{\left( {\sqrt 5 } \right)}^2}}}{{2\sqrt 5 }} = \frac{{\sqrt 5 }}{2};$

$\frac{1}{{3\sqrt {20} }} = \frac{1}{{3\sqrt {4.5} }} = \frac{1}{{6\sqrt 5 }} = \frac{{\sqrt 5 }}{{30}};$

$\frac{{2\sqrt 2 + 2}}{{5\sqrt 2 }} = \frac{{\sqrt 2 \left( {2 + \sqrt 2 } \right)}}{{5\sqrt 2 }} = \frac{{2 + \sqrt 2 }}{5};$

$\frac{{y + b\sqrt y }}{{b\sqrt y }} = \frac{{\sqrt y \left( {\sqrt y + b} \right)}}{{b\sqrt y }} = \frac{{\sqrt y + b}}{b}.$

b) $\frac{3}{{\sqrt 3 + 1}} = \frac{{3\left( {\sqrt 3 - 1} \right)}}{{3 - 1}} = \frac{{3\left( {\sqrt 3 - 1} \right)}}{2};$

$\frac{2}{{\sqrt 3 - 1}} = \frac{{2\left( {\sqrt 3 + 1} \right)}}{{\left( {\sqrt 3 - 1} \right)\left( {\sqrt 3 + 1} \right)}} = \sqrt 3 + 1;$

$\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} = \frac{{{{\left( {2 + \sqrt 3 } \right)}^2}}}{{\left( {2 + \sqrt 3 } \right)\left( {2 - \sqrt 3 } \right)}} = \frac{{7 + 4\sqrt 3 }}{{4 - 3}} = 7 + 4\sqrt 3 ;$

$\frac{b}{{3 + \sqrt b }} = \frac{{b\left( {3 - \sqrt b } \right)}}{{9 - b}};$ $\frac{p}{{2\sqrt p - 1}} = \frac{{p\left( {2\sqrt p + 1} \right)}}{{4p - 1}} = \frac{{2p\sqrt p + p}}{{4p - 1}};$

c) $\frac{2}{{\sqrt 6 - \sqrt 5 }} = 2\left( {\sqrt 6 + \sqrt 5 } \right);$

$\frac{3}{{\sqrt {10} + \sqrt 7 }} = \frac{{3\left( {\sqrt {10} - \sqrt 7 } \right)}}{{10 - 7}} = \sqrt {10} - \sqrt 7 ;$

$\frac{1}{{\sqrt x - \sqrt y }} = \frac{{\sqrt x + \sqrt y }}{{x - y}};$

$\frac{{2ab}}{{\sqrt a - \sqrt b }} = \frac{{2ab\left( {\sqrt a + \sqrt b } \right)}}{{a - b}}.$