Find the perimeter of a square whose diagonal is √6.

According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse, in other words, the sum of the squares of the sides of a square is equal to the square of its diagonal. The sum of the squares of the sides of a given square is equal to the square of the square root of 6. It turns out that the sum of the squares of the sides is 6. Since the sides of the square are equal to each other, we compose the equation:

a ^ 2 + a ^ 2 = 6;

a * a * a * a = 6;

a ^ 4 = 6;

a = 4√ 6.