Question

Rationalise the denominator of √3-1/√3+1​

Answer 1

Answer:

Step-by-step explanation:

We need to rationalize the givenequation

To rationalize we will multiply and divide the denominator by √3+1

(√3+1)√3+1)/(√3-1)(√3+1)

Denominator can be simplified using the identity (a2-b2)=(a-b)(a+b)

And the equation becomes

=(√3+1)2/(√3)2-(1)2

=(4+2√3)/2

=2+√3

Answer 2

Step-by-step explanation:

$\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \\ \sf \leadsto \frac{( \sqrt{3} - 1)( \sqrt{3} - 1)}{( \sqrt{3} + 1)( \sqrt{3} - 1) } \\ \sf \leadsto \frac{( \sqrt{3} - 1) {}^{2} }{( \sqrt{3 {)}}^{2} - { (1)}^{2} } \\ \sf \leadsto \frac{ {\sqrt{3} }^{2} - 2 .\sqrt{3}.1 + {1}^{2} }{3 - 1} \\ \sf \leadsto \frac{3 - 2 \sqrt{3} + 1 }{2} \\ \sf \leadsto \frac{2 - 2 \sqrt{3} }{2} \\ \sf \leadsto \frac{2(1 - \sqrt{3} )}{2} \\ \bf \leadsto 1 - \sqrt{3}$