Can we measure under root 2 exactly and if yes then how?

The exact measure of it is the length of diagonal of a square with length of side 1

The square root of2, written in mathematics as √2 or 21⁄2, is the positive algebraic number that, when multiplied by itself, gives the number2. Technically, it is called the principal square root of2, to distinguish it from the negative number with the same property.