Question

Write the conjugate of the following surds : 2+√5

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Answer 1

༒࿐៚ Answer ༒࿐៚

We Know that the When Sum of two terms and the difference of the Same two terms are multipled, the Product is always a rational Number.

Let us applied this Concept two a binomial Surd :- (2+√5)

When we Multiply this with the difference of the same two terms,that is, with (2+√5), the Product is:

$(2 + \sqrt{5} )(2 - \sqrt{5} ) = (2 {)}^{2} - ( \sqrt{5} {)}^{2} = 5 - 4 = 1$

$( {a}^{2} - {b}^{2} = (a + b)(a - b))$

Since, 1 is a rational Number. Hence (2-√5) is the Conjugate of (2+√5)

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