Simplify:
(√6−√5√6+√5+√6+√5√6−√5)(6−56+5+6+56−5)


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Answer:

2222

Step by Step Explanation:
  1. Let us multiply the numerator and denominator of √6−√5√6+√56−56+5 by its rationalising factor.(6−5)(6+5)×(6−5)(6−5)= (6−5)2(6+5)(6−5)= (6)2+(5)2−2×6×5(6)2−(5)2[(a−b)2=a2+b2−2ab and (a+b)(a−b)=a2−b2]= 6+5−2306−5= 11−230
  2. Similarly, let us multiply the numerator and denominator of (6+5)(6−5) by its rationalising factor. (6+5)(6−5)×(6+5)(6+5)= (6+5)2(6−5)(6+5)= (6)2+(5)2+2×6×5(6)2−(5)2[(a+b)2=a2+b2+2ab and (a+b)(a−b)=a2−b2]= 6+5+2306−5= 11+230
  3. Thus, (6−56+5+6+56−5)=11−230+11+230=22

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