Question

The simplest rationalisation factor of root 3 + root 5

Answer 1

Answer:

answer is

$\sqrt{3} - \sqrt{5 }$

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Answer 2

Answer:

$\sqrt{3} - \sqrt{5}$ is the simplest rationalisation factor of $\sqrt{3} + \sqrt{5}$ .

Step-by-step explanation:

Explanation:

Given , $\sqrt{3} + \sqrt{5}$

Rationalisation factor -If the product of two irrational numbers, is a rational number, then each irrational  acts as a rationalizer for the other.

And we know the simplest  rationalisation factor of

($\sqrt{a} +\sqrt{b}$) is ($\sqrt{a} - \sqrt{b}$).

Step 1:

We have $\sqrt{3} + \sqrt{5}$ ,

If we multiple ($\sqrt{3} - \sqrt{5}$) with ($\sqrt{3} + \sqrt{5}$) we get ,

$(\sqrt{3} + \sqrt{5})(\sqrt{3} - \sqrt{5})$

⇒$(\sqrt{3} )^{2} - (\sqrt{5} )^{2}$                [∴$a^{2} - b^2 = (a+b)(a-b)$]

⇒3 - 5 = -2

And -2 is a rational number .

Final answer :

Hence , the simplest rationalisation factor of $\sqrt{3} + \sqrt{5}$ is ($\sqrt{3} - \sqrt{5}$).

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