Question

the simplest rationalising factor of 2√5-√3 is



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Answer 1

Answer:2√5+√3

Step-by-step explanation:

2√5-√3 × 2√5+√3=4√5√5 + 2√5√3 - 2√5√3-√3√3

                               =4*5 - 3        (2√5√3 & -2√5√3 get cancelled)

                               =20-3

                               =17

               ∴ It is rationalized

                       Therefore the simplest rationalizing factor of

                            2√5-√3 is  2√5+√3.

                                                                               

Answer 2

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

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 $a\sqrt{b} \ - \ \sqrt{c}$ will be $a\sqrt{b} \ + \ \sqrt{c}$

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

Similarly,

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

⇒ $4(5) - 3 = 20 - 3 = 17$, which is rational

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