Question

Find the rationalizing factor of 7-2√3​

Answer 1

rationalizing factor of 7-2√3 is its reciprocal.

Answer 2

Given: $7 - 2\sqrt{3}$

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

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

Similarly,

∴ $(7 - 2\sqrt{3}) (7 \ + 2\sqrt{3}) = (7)^{2} - (2\sqrt{3}) ^{2}$

⇒ $49 - 4(3) = 49 - 12 = 37$, which is rational

Hence, rationalisation factor of  $7 - 2\sqrt{3}$  is  $7 + 2\sqrt{3}$.