Write the conjugates of the binomial surd 10√2+3√5
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 (10√2+3√5).
When we multiply this with the difference of the same two terms, that is, with (10√2−3√5), the product is:
(10√2+3√5)(10√2−3√5)=(10√2)2−(3√5)2=(10×2)−(3×5)=20−15=5(∵a2−b2=(a+b)(a−b))
Since 5 is a rational number.
Hence, (10√2−3√5) is the conjugate of (10√2+3√5).