Write the conjugates of binomial surd given as √a+√b
We know that the when sum of two terms and the difference of the same two terms are multiplied, the product is always a rational number.
Let us apply this concept to a binomial surd (√a+√b).
When we multiply this with the difference of the same two terms, that is, with (√a−√b), the product is:
(√a+√b)(√a−√b)=(√a)2−(√b)2=a−b(∵a2−b2=(a+b)(a−b))
Since a−b is a rational number.
Hence, (√a−√b) is the conjugate of (√a+√b).