Answer :

Formula used.


(a – b)2 = a2 – 2ab + b2


1st value is √7 + 1


Its square is


(√7 + 1)2 = (√7)2 + 12 + 2 × 1 × √7 = 7 + 1 + 2√7 = 8 + 2√7


2nd value is √5 + √3


Its square is


(√5 + √3)2 = (√5)2 + (√3)2 + 2 × √3 × √5 = 5 + 3 + 2√15 = 8 + 2√15


If 7<15


Then √7 < √15


Then 8 + √7 < 8 + √15


Then √(8 + √7) < √(8 + √15)


√7 + 1 < √5 + √3


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