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(A) To find the rationalising factor of an expression of the form $a - \sqrt{b}$,we multiply it by its conjugate $a + \sqrt{b}$ such that the product

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$-2+\sqrt{5}$

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(A) To find the rationalising factor of an expression of the form $a - \sqrt{b}$,we multiply it by its conjugate $a + \sqrt{b}$ such that the product is a rational number.Given the expression $-2 - \sqrt{5}$.Let the rationalising factor be $x$.We know that $(-2 - \sqrt{5}) 	imes (-2 + \sqrt{5}) = (-2)^2 - (\sqrt{5})^2$.$= 4 - 5 = -1$.Since $-1$ is a rational number,the expression $-2 + \sqrt{5}$ is the rationalising factor.Alternatively,we can also multiply by $2 + \sqrt{5}$:$(-2 - \sqrt{5}) 	imes (2 + \sqrt{5}) = -(2 + \sqrt{5}) 	imes (2 + \sqrt{5}) = -(4 + 5 + 4\sqrt{5}) = -(9 + 4\sqrt{5})$,which is not rational.Therefore,the correct rationalising factor is $-2 + \sqrt{5}$.

The rationalising factor of $-2-\sqrt{5}$ is ..............

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