La diagonal de las caras de un cubo mide 6 cm ; calcular la diagonal del cubo?

Respuesta : <img src="https://tex.z-dn.net/?f=%5Ctexttt%7BLa%20diagonal%20del%20cubo%20mide%3A%7D%5C%5C3%5Csqrt%7B6%7D" />Explicación paso a paso : <img src="https://tex.z-dn.net/?f=%5Ctexttt%7BComo%20la%20diagonal%20b%20de%20las%20caras%20de%20un%20cubo%7D%5C%5C%5Ctexttt%7Bde%20lado%20a%20mide%206%20cm%2C%20entonces%7D%5C%5C%5Ctexttt%7Bpor%20el%20teorema%20de%20Pit%5C%27agoras%20se%20tiene%3A%7D%5C%5C%5C%5Cb%5E%7B2%7D%3Da%5E%7B2%7D%2Ba%5E%7B2%7D%5C%5Cb%3D%5Csqrt%7Ba%5E%7B2%7D%2Ba%5E%7B2%7D%7D%5C%5Cb%3D%5Csqrt%7B2a%5E%7B2%7D%7D%5C%5C6%3D%5Csqrt%7B2a%5E%7B2%7D%7D%5C%5C%5Ctexttt%7BElevando%20al%20cuadrado%20toda%20la%20expresi%5C%27on%3A%7D%5C%5C%286%29%5E%7B2%7D%3D%28%5Csqrt%7B2a%5E%7B2%7D%7D%29%5E%7B2%7D%5C%5C36%3D2a%5E%7B2%7D%5C%5C%5Ctexttt%7BDespejando%20a%3A%7D%5C%5Ca%5E%7B2%7D%3D%5Cfrac%7B36%7D%7B2%7D%3D18%5C%5Ca%3D%5Csqrt%7B18%7D%3D3%5Csqrt%7B2%7D" /><img src="https://tex.z-dn.net/?f=%5Ctexttt%7BComo%20los%20lados%20miden%3A%7D%5C%2C%5C%2C3%5Csqrt%7B2%7D%5C%2C%5C%2C%5Ctexttt%7By%20la%20hipotenusa%20o%20diagonal%20mide%3A%7D%5C%2C%5C%2C6%5C%2Ccm%5C%5C%5Ctexttt%7Bentonces%2C%20aplicando%20nuevamente%20el%20teorema%20de%20Pit%5C%27agoras%7D%5C%5C%5Ctexttt%7Bpara%20hallar%20la%20diagonal%20c%20del%20cubo%7D%5C%5C%5Ctexttt%7Bnos%20queda%3A%7D" /><img src="https://tex.z-dn.net/?f=c%5E%7B2%7D%3Da%5E%7B2%7D%2Bb%5E%7B2%7D%5C%5Cc%3D%5Csqrt%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D%5C%5Cc%3D%5Csqrt%7B%283%5Csqrt%7B2%7D%29%5E%7B2%7D%2B%286%29%5E%7B2%7D%7D%5C%5Cc%3D%5Csqrt%7B18%2B36%7D%5C%5Cc%3D%5Csqrt%7B54%7D%3D%5Csqrt%7B%286%29%289%29%7D%5C%5Cc%3D%5Csqrt%7B6%7D%5Csqrt%7B9%7D%3D3%5Csqrt%7B6%7D" />.