<h2>Answer: To establish a commercial route between Portugal and India
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During the fifteenth century the commercial route of spices from India (Asia) to Europe was monopolized by the Arabs. Before it was Italy that dominated this trade, but after the capture of Constantinople by the Ottomans in 1453, this changed, resulting in a more expensive purchase of spices for Europe (Portugal specifically, in this case).
However, in Portugal, the idea of carrying out an exploratory expedition to these Indian lands and inaugurating a new commercial route was already underway. Since the Portuguese navigator Bartolomé Díaz had managed to reach the Indian Ocean by crossing the southern tip of Africa through the Atlantic Ocean. Therefore, that part of the route was already known.
It is then how, after planning, studies and some unsuccessful attempt to start with such an ambitious expedition, the newly appointed king of Portugal, Manuel I, appointed Vasco da Gama to lead that expedition.
<h2>The initial idea was to reach India around the southern edge of the African continent, passing by the Cape of Good Hope and go in search of India in order to establish a safe and reliable maritime route.
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Then, on July 8th, 1497, Vasco da Gama sailed, in what would be his first trip to Asian lands, from the port of Santa Maria de Belém, on the banks of the Tagus River in Lisbon and on May 20th, 1498, his fleet arrived near Calicut, India. After which the sea route was established from Europe to India.