Question

Rationalize the denominator √11-√7upon√11+√7

Answer 1

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Answer 2

Question:

Rationalize the denominator of ;

(√11 - √7) / (√11 + √7)

Answer:

(9 - √77) / 2

Solution:

We have ;

=> (√11 - √7)(√11 - √7)/(√11 + √7)(√11 - √7)

=> (√11 - √7)² / [ (√11)² - (√7)² ]

=> [ (√11)² - 2•√11•√7 + (√7)² ] / (11 - 7)

=> ( 11 - 2√77 + 7 ) / 4

=> ( 18 - 2√77 ) / 4

=> 2•( 9 - √77 ) / 4

=> (9 - √77) / 2

Hence,

Required expression is ;

(9 - √77) / 2