Question

rationalise the
denominator ;

root 7 - root 5 / root7 +root 5



​

Answer 1

Answer:

$6 - \sqrt{35}$

Step-by-step explanation:

$= \frac{\sqrt{7}- \sqrt{5} }{\sqrt{7} +\sqrt{5} }\\\\= \frac{\sqrt{7}- \sqrt{5} }{\sqrt{7} +\sqrt{5} }*\frac{\sqrt{7}- \sqrt{5} }{\sqrt{7} -\sqrt{5}}\\\\= \frac{(\sqrt{7}-\sqrt{5})^{2} }{(\sqrt{7})^{2}-(\sqrt{5})^{2} }\\\\= \frac{(\sqrt{7})^{2}- (2*\sqrt{7}*\sqrt{5})+(\sqrt{5})^{2} }{7 - 5}\\\\= \frac{7-2\sqrt{35}+5}{2}\\\\= \frac{12-2\sqrt{35} }{2}\\\\as~2~is~divisable~by~both~2~and~12~we~can~simplify~it...\\\\= 6 - \sqrt{35}$

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