Nomor 1
[tex] \boxed{\begin{aligned}\sf \frac{2}{ \sqrt{6} } &=\sf \frac{2}{ \sqrt{6} } \times \frac{ \sqrt{6} }{ \sqrt{6} } \\ \sf &=\sf \frac{2 \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } \\ \sf &= \sf \frac{2 \sqrt{6} }{6} \\ \sf &=\sf \frac{ \sqrt{6} }{3} \end{aligned}}[/tex]
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Nomor 2
[tex] \boxed{\begin{aligned}\sf \frac{3}{ \sqrt{5} } &=\sf \frac{3}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ \sf &=\sf \frac{3 \sqrt{5} }{ \sqrt{5} \times \sqrt{5} } \\ \sf &= \sf \frac{3 \sqrt{5} }{5} \end{aligned}}[/tex]
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Nomor 3
[tex] \boxed{\begin{aligned}\sf \frac{6}{5 - \sqrt{3} } &=\sf \frac{6}{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } \\ \sf &=\sf \frac{6 \: (5 + \sqrt{3}) }{(5 - \sqrt{3})(5 + \sqrt{3} ) } \\ \sf &= \sf \frac{6 \: (5 + \sqrt{3} )}{25 - 3} \\ \sf &=\sf \frac{6 \: (5 + \sqrt{3} )}{22} \\ \sf &=\sf \frac{3 \: (5+ \sqrt{3} )}{11}\\ \sf &=\sf \frac{15+ 3\sqrt{3} )}{11}\end{aligned}}[/tex]
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Nomor 4
[tex] \boxed{\begin{aligned}\sf \frac{5}{5 + \sqrt{2} } &=\sf \frac{5}{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} } \\ \sf &=\sf \frac{5 \: (5 - \sqrt{2} )}{(5 + \sqrt{2})(5 - \sqrt{2} )} \\ \sf &= \sf \frac{25 - 5 \sqrt{2} }{25 - 2} \\ \sf &=\sf \frac{25 - 5 \sqrt{2} }{23} \end{aligned}}[/tex]
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Nomor 5
[tex] \boxed{\begin{aligned}\sf \frac{ \sqrt{5} }{ \sqrt{7} } &=\sf \frac{ \sqrt{5} }{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } \\ \sf &=\sf \frac{ \sqrt{5} \times \sqrt{7} }{ \sqrt{7} \times \sqrt{7} } \\ \sf &= \sf \frac{ \sqrt{35} }{7} \end{aligned}}[/tex]
Bentuk AKar
Rasional
Penjelasan dengan langkah-langkah:
[tex]\sf 1). \dfrac{2}{\sqrt5} = \\[/tex]
[tex]\sf =\dfrac{2\sqrt5}{5} = \dfrac{2}{5}\sqrt 5\\[/tex]
[tex]\sf 2) \dfrac{3}{\sqrt 5} =[/tex]
[tex]\sf = \dfrac{3\sqrt 5}{5}= \dfrac{3}{5}\sqrt 5\\\\[/tex]
[tex]\sf 3) \dfrac{6}{5-\sqrt 3}=[/tex]
[tex]\sf = \dfrac{6(5 + \sqrt 3)}{(5-\sqrt 3)(5+\sqrt 3)}[/tex]
[tex]\sf = \dfrac{6(5 + \sqrt 3)}{25-3}[/tex]
[tex]\sf = \dfrac{6(5 + \sqrt 3)}{22}[/tex]
[tex]\sf = \dfrac{3}{11}(5 + \sqrt 3)\\\\[/tex]
[tex]\sf 4) \dfrac{5}{5+\sqrt 2}=[/tex]
[tex]\sf = \dfrac{5(5-\sqrt 2)}{(5+\sqrt 2)(5-\sqrt2)}[/tex]
[tex]\sf = \dfrac{5(5-\sqrt 2)}{25-2}[/tex]
[tex]\sf = \dfrac{5(5-\sqrt 2)}{23}[/tex]
[tex]\sf = \dfrac{5}{23}(5-\sqrt 2)\\\\[/tex]
[tex]5. \sf \dfrac{\sqrt 5}{\sqrt7} =[/tex]
[tex]\sf = \dfrac{\sqrt 5(\sqrt 7)}{\sqrt7(\sqrt7)}[/tex]
[tex]\sf = \dfrac{\sqrt {35}}{7}[/tex]
[tex]\sf = \dfrac{1}{7} \sqrt {35}\\\\[/tex]
