Can you give me example to prove that the conjugate pairs are always rational number
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The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.
Conjugate surds are also known as complementary surds.
Thus, the sum and the difference of two simple quadratic surds 4√7and √2 are 4√7 + √2 and 4√7 - √2 respectively. Therefore, two surds (4√7 + √2) and (4√7 - √2) are conjugate to each other.
Similarly, two surds (-2√5 + √3) and (-2√5 - √3) are conjugate to each other.
In general, two binomial quadratic surds (x√a + y√b) and (x√a - y√b) are conjugate to each other.
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