Question

rationalize the denominator root 11- root 7 / root 11 + root 7​

Answer 1

Answer:

The answer is$\frac{18 + 2 \sqrt{77} }{3}$ .

Step-by-step explanation:

$\frac{ \sqrt{11} - \sqrt{7} }{ \sqrt{11} + \sqrt{7} } \\ = \frac{( \sqrt{11} - \sqrt{7})( \sqrt{11} - \sqrt{7}) }{( \sqrt{11} + \sqrt{7})( \sqrt{11} - \sqrt{7}) } \\ = \frac{ ({ \sqrt{11} - \sqrt{7}) }^{2} }{ { (\sqrt{11}) }^{2} - ({ \sqrt{7} )}^{2} } \\ = \frac{( { \sqrt{11} )}^{2} + ( { \sqrt{7} )}^{2} - (2 \sqrt{11} \sqrt{7} ) }{11 - 7} \\ = \frac{11 + 7 + 2 \sqrt{77} }{3} \\ = \frac{18 + 2 \sqrt{77} }{3}$

Answer 2

Answer:

Step-by-step explanation:

/* Rationalising the denominator, we get

/* By algebraic identities:

i) (a-b)² = a²+b²-2ab

ii) (a+b)(a-b) = a² - b² */

Therefore,

/* Compare both sides, we get

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