Which among the following is greatest `sqrt7 + sqrt3, sqrt5 + sqrt5, sqrt6 +2 ?`

Explanation

Let `x = sqrt7+sqrt3`

Let `y = sqrt5+sqrt5`

Let `z = sqrt6 +2 = sqrt6 + sqrt4`

Now, `x^2 = (sqrt7+sqrt3)^2 = 7+3+2sqrt21 = 10+2sqrt21`

`y^2 = (sqrt5+sqrt5)^2 = 5+5+2sqrt25 = 10+2sqrt25`

`z^2 = (sqrt6+sqrt4)^2 = 6+4+2sqrt24 = 10+2sqrt24`

So, `y^2` is the largest. Thus, `y` is the largest.

So, largest of the given number is `sqrt5+sqrt5`.