Question

rationalising factor of 2√3-5√2 is

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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: $2\sqrt{3} - 5\sqrt{2}$

To find: Rationalisation factor of the given expression

Solution:

Rationalisation factor is an irrational number that is multiplied with the given irrational expression to make it free from square roots.

Now, the rationalisation factor of $\sqrt{x} \ - \ \sqrt{y}$ will be $\sqrt{x} \ + \ \sqrt{y}$

∵ $(\sqrt{x} \ - \ \sqrt{y} )(\sqrt{x} \ + \ \sqrt{y} ) = (\sqrt{x}) ^{2} \ - \ (\sqrt{y}) ^{2} = x - y$, which is rational (free from roots)

Similarly,

∴ $(2\sqrt{3} - 5\sqrt{2}) (2\sqrt{3} + 5\sqrt{2}) = (2\sqrt{3} )^{2} - (5\sqrt{2}) ^{2}$

⇒ $4(3) - 25(2) = 12 - 50 = -38$, which is rational

Hence, rationalisation factor of  $2\sqrt{3} - 5\sqrt{2}$  is  $(2\sqrt{3} + 5\sqrt{2})$.