Question

5+root 6/5-root6 rationalise
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Answer 1

Answer:

$to \: rationalize \\ \frac{5 + \sqrt{6} }{5 - \sqrt{6} } \times \frac{5 + \sqrt{6} }{5 + \sqrt{6} } \\ = \frac{(5 + \sqrt{6} ) {}^{2} }{(5) {}^{2} - ( \sqrt{6} ) {}^{2} } \\ = \frac{ (5) {}^{2} + ( \sqrt{6} ) {}^{2} + 2 \times 5 \times \sqrt{6} }{25 - 6} \\ = \frac{25 + 6 + 10 \sqrt{6} }{19} \\ = \frac{31 + 10 \sqrt{6} }{19}$

USED IDENTITIES :-

(a+b)²=a²+b²+2ab

a²-b²=(a+b)(a-b)

Answer 2

Answer:

(31+10√6)/19

Step-by-step explanation:

5+√6/5-√6

= 5+√6/5-√6 × 5+√6/5+√6

= (5+√6)²/5²-√6²

= 5²+√6²+2(5×√6)/ 25-6

= 25+6+10√6/19

=31+10√6/19

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