show that 2-√3 is a irrational number
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Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago.[24] Their long occupation, initially in varying forms of isolation as hunter-gatherers, has made the region highly diverse, second only to Africa in human genetic diversity.[25] Settled life emerged on the subcontinent in the western margins of the Indus river basin 9,000 years ago, evolving gradually into the Indus Valley Civilisation of the third millennium BCE.[26] By 1200 BCE, an archaic form of Sanskrit, an Indo-European language, had diffused into India from the northwest, unfolding as the language of the Rigveda, and recording the dawning of Hinduism in India.[27] The Dravidian languages of India were supplanted in the northern and western regions.[28] By 400 BCE, stratification and exclusion by caste had emerged within Hinduism,[29] and Buddhism and Jainism had arisen, proclaiming social orders unlinked to heredity.[30] Early political consolidations gave rise to the loose-knit Maurya and Gupta Empires based in the Ganges Basin.[31] Their collective era was suffused with wide-ranging creativity,[32] but also marked by the declining status of women,[33] and the incorporation of untouchability into an organised system of belief.[g][34] In South India, the Middle kingdoms exported Dravidian-languages scripts and religious cultures to the kingdoms of Southeast Asia