Question

Rationalise 7-√3/7+√3

Answer 1

↬$\frac{7 - \sqrt{3} }{7 + \sqrt{3} }$

↬$\frac{7 - \sqrt{3} }{7 + \sqrt{3} } \times \frac{7 - \sqrt{3} }{7 - \sqrt{3} }$

↬$\frac{ ( {7 - \sqrt{3} })^{2} }{( {7})^{2} - { (\sqrt{3} })^{2} }$

↬$\frac{( {7})^{2} - 2 \times 7 \times \sqrt{3} + ( { \sqrt{3} })^{2} }{49 - 3}$

↬$\frac{49 - 14 \sqrt{3} + 3}{46}$

↬$\frac{52 - 14 \sqrt{3} }{46}$

↬$\frac{2(26 - 7 \sqrt{3} )}{46}$

↬$\frac{26 - 7 \sqrt{3} }{23}$

Note:

ඞ $( {a - b})^{2} = {a}^{2} - 2 ab+ {b}^{2}$

ඞ $(a + b)(a - b) = {a}^{2} - {b}^{2}$

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