Let us write which one is greater of and

Formula used.

(a – b)² = a² – 2ab + b²

1^st value is √7 + 1

Its square is

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

2^nd 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