Question

rationalise the denominator and simplify 1 by 7 - √ 5​

Answer 1

Step-by-step explanation:

$\frac{1}{7 - \sqrt{5} } \\ \\ = \geqslant \frac{1}{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} } \\ \\ = \geqslant \frac{7 + \sqrt{5} }{(7) {}^{2} - ( \sqrt{5} ) {}^{2} } \\ \\ = \geqslant \frac{7 + \sqrt{5} }{49 - 5} \\ \\ = \geqslant \frac{7 + \sqrt{5} }{44}$

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\dashrightarrow \dfrac{1}{7-\sqrt{5}}$

$\large\underline\bold{TO\:RATIONALISE\:THE\: DENOMINATOR,}$

✯. IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: (a+b)(a-b)=a^2-b^2\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\dashrightarrow \dfrac{1}{7-\sqrt{5}}$

$\therefore multiplying\: denominator\:and\:numerator\:by\: 7+\sqrt{5}.we\:get,$

$\implies \dfrac{1}{7-\sqrt{5}} \times \dfrac{7+\sqrt{5}}{7+\sqrt{5}}$

$\implies \dfrac{7+\sqrt{5}}{(7-\sqrt{5})(7+\sqrt{5})}$

$\implies \dfrac{7+\sqrt{5}}{[ (7)^2-(\sqrt{5})^2]}\:--\boxed{from\:given\:identity.}$

$\implies \dfrac{7+\sqrt{5}}{49-5}$

$\implies \dfrac{7+\sqrt{5}}{44}$

$\large{\boxed{\bf{ \star\:\:\dfrac{7+\sqrt{5}}{44} \:\: \star}}}$

$\large\underline\bold{RATIONALISED\: DENOMINATOR\:IS\: \dfrac{7+\sqrt{5}}{44}}$

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