Two surds are said to be conjugate of each other if their product gives rise to a rational number. From our knowledge of difference of two squares, we know that:
(a + b)(a - b) = a² - b² Similarly,
(√a+√b)(√a-√b) = a² - b²
While √a + √b and √a - √b are not rational, their product (a²-b²) is rational. Hence, √a+√b and √a-√b are conjugates of each other.

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