Question

e) Simplify:
i)1/1+√2
ii)7+√3/7-√3
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Answer 1

Step-by-step explanation:

i) $\frac{1}{1+\sqrt{2} }$

$=\frac{1}{1+\sqrt{2} } *\frac{1-\sqrt{2}}{1-\sqrt{2}} \\=\frac{1-\sqrt{2}}{1^{2}-(\sqrt{2})^{2} }\\=\frac{1-\sqrt{2}}{1-2} \\= - (1-\sqrt{2})$

ii)$\frac{7+\sqrt{3} }{7-\sqrt{3}}$

$=\frac{7+\sqrt{3} }{7-\sqrt{3}}*\frac{7+\sqrt{3} }{7+\sqrt{3}}\\\\=\frac{(7+\sqrt{3} )^{2}}{7^{2}-(\sqrt{3})^{2}}\\\\=\frac{49+14\sqrt{3}+3 }{49-3}\\\\=\frac{52+14\sqrt{3}}{46} \\=\frac{2( 26+7\sqrt{3})}{46} \\=\frac{26+7\sqrt{3}}{23}$