Simplify:
(√6−√5√6+√5+√6+√5√6−√5)


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Answer:

22

Step by Step Explanation:
  1. 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+5−2√306−5= 11−2√30
  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+2√306−5= 11+2√30
  3. Thus, (√6−√5√6+√5+√6+√5√6−√5)=11−2√30+11+2√30=22

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