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7+√48 = 7+√4×4×3 = 7+4√3

let it is the square of a+√b. (there must be in that format or you can see from the options also. All are in a+√b format)

so (a+√b)² = 7+4√3

(a+√b)² = a²+b + 2a√b = 7+4√3

comparing the terms,

2a√b = 4√3

⇒ a√b = 2√3

a=2, b=3

and it satisfies a²+b = 7

So the required number is a+√b = 2+√3

let it is the square of a+√b. (there must be in that format or you can see from the options also. All are in a+√b format)

so (a+√b)² = 7+4√3

(a+√b)² = a²+b + 2a√b = 7+4√3

comparing the terms,

2a√b = 4√3

⇒ a√b = 2√3

a=2, b=3

and it satisfies a²+b = 7

So the required number is a+√b = 2+√3

*We have 7+√48*

*= 4+3+√4×4×3*

*= 2²+ (√3)²+2*2*√3*

*= (2+ √3)²*

*Hence the square root is +(2+√3)*
(C) 2 +√ 3 (D) 3 +√ 2