prove that under root x + under root y is a irrational number
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Assume that √x+√y is an rational number
Therefore √x+√y= p/q, where p and q are coprimes and q≠0
therefore,
(√x+√y)² = (p/q)²
⇒ x +2√xy +y = (p/q)²
⇒√xy = p²/q² - (x+y)
here LHS is irrational where as RHS is rational
∴LHS≠RHS
∴Our assumption is wrong
∴√x+√y is irrational
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