The hypotenuse of an isosceles right-angled triangle is 8 cm. Find its legs.

According to the Pythagorean theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the legs of this triangle. Because the triangle is isosceles, then the legs are equal to each other (we denote the length of the leg x).
Then:
x ^ 2 + x ^ 2 = 8 * 8;
2x ^ 2 = 64;
x ^ 2 = 32;
x = 32 ^ 0.5 = 4 2 ^ 0.5.