How to replace one part of list of lists

Here are a few ways:

MapAt[Sqrt, data, {All, 1}]

Replace[data, {x_, y___} :> {Sqrt[x], y}, {1}]

data // Query[All, {1 -> Sqrt}]

SubsetMap[Sqrt, data, {All, 1}]

ReplacePart[data, {i_, 1} :> Sqrt[data[[i, 1]]]]

data2 = data;
data2[[All, 1]] = Sqrt[data2[[All, 1]]];
data2

☺ = {#^(1/2), ##2} &;

☺ @@@ data

{{7, 35, 14}, {8, 40, 16}, {9, 45, 18}}

or

☺☺ = {#^(1/2), ##2} & @@@ # &;

☺☺ @ data

{{7, 35, 14}, {8, 40, 16}, {9, 45, 18}}

What kglr posted, but a bit more "golfed"

data = {{49, 35, 14}, {64, 40, 16}, {81, 45, 18}};

{√#, ##2} & @@@ data

{{7, 35, 14}, {8, 40, 16}, {9, 45, 18}}