Question

plz answer this question ​

Answer 1

Given:

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

$Here, \sqrt{2}$$= 1.414 \: and \: \sqrt{3}$= 1.732

$We \: have \: to \: find, \: the \: value \: of \: \dfrac{1}{\sqrt{3}-\sqrt{2}}$

Solution:

$∴ \dfrac{1}{\sqrt{3}-\sqrt{2}}$

Rationalising numerator and denominator, we get

$=\dfrac{1}{\sqrt{3}-\sqrt{2}}\times \dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

Using the algebraic identity:

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

$=\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}^2-\sqrt{2}^2}$

$=\dfrac{\sqrt{3}+\sqrt{2}}{3-2}$

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

$= \sqrt{3} + \sqrt{2}$

$Put \: \sqrt{2} \: = 1.414 \: and \: \sqrt{3} = 1.732,$

we get,

= 1.732 + 1.414

= 3.146

$∴ \dfrac{1}{\sqrt{3}-\sqrt{2}} = 3.146$

$Thus, \: the \: value \: of \: \dfrac{1}{\sqrt{3}-\sqrt{2}} \: is \: equal \: to \: 3.146.$