Question

Rationalise 1/(√3-√2)+1

Answer 1

Hey there!

Given radical expression to rationalize "1/(_/3 - _/2) + 1"

Multiply the radical expression excluding value of "1" (or not taking in process of conjugation):

Conjugate here, is;     $\bf{\dfrac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

$\bf{\dfrac{1 \times (\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})} + 1}$

Apply the basic difference rule of Two Squares formula that is (In Denominator):

$\bf{(a - b) (a + b) = a^2 - b^2}$

Here, a = _/3  and  b = _/2.

Therefore,

$\bf{\dfrac{\sqrt{3} + \sqrt{2}}{(\sqrt{3})^2 - (\sqrt{2})^2} + 1}$

$\bf{\dfrac{\sqrt{3} + \sqrt{2}}{3 - 2} + 1}$

$\bf{\dfrac{\sqrt{3} + \sqrt{2}}{1} + 1}$

$\boxed{\bf{\underline{\therefore \quad Rationalized \: Term = \sqrt{3} + \sqrt{2} + 1}}}$

Which is the required solution for this type of query

Hope this helps you and solves your doubts for rationalization of terms!!!!