Jawab:
[tex]\frac{5 \sqrt{2} - \sqrt{14} }{18}[/tex]
Penjelasan dengan langkah-langkah:
[tex]\frac{\sqrt{2} }{5 + \sqrt{7}} = \frac{\sqrt{2} }{5 + \sqrt{7}} \times \frac{5 - \sqrt{7}}{5 - \sqrt{7}}[/tex]
[tex]= \frac{\sqrt{2}(5 - \sqrt{7}) }{(5)^2 - (\sqrt{7})^2} \\ \\= \frac{\sqrt{2}(5 - \sqrt{7}) }{25 - 7} \\ \\= \frac{5 \sqrt{2} - \sqrt{14} }{18}[/tex]
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Verified answer
Jawab:
[tex]\frac{5 \sqrt{2} - \sqrt{14} }{18}[/tex]
Penjelasan dengan langkah-langkah:
[tex]\frac{\sqrt{2} }{5 + \sqrt{7}} = \frac{\sqrt{2} }{5 + \sqrt{7}} \times \frac{5 - \sqrt{7}}{5 - \sqrt{7}}[/tex]
[tex]= \frac{\sqrt{2}(5 - \sqrt{7}) }{(5)^2 - (\sqrt{7})^2} \\ \\= \frac{\sqrt{2}(5 - \sqrt{7}) }{25 - 7} \\ \\= \frac{5 \sqrt{2} - \sqrt{14} }{18}[/tex]