Question

The positive square root of 7 √ 48 is

Answer 1

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

Answer 2

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)