Question

Write the rationalising factor of the denominator in 1/root2 +root3

Answer 1

Answer:

1/√2+√3×√2-√3/√2-√3

√2-√3/(√2-√3)^2

√2-√3/(√2)^2-2(√2)(√3)+(√3)^2

√2-√3/2-2(√6)+3

√2-√3/2√6

Answer 2

$\frac{1}{\sqrt{2} + \sqrt{3} }$

multiplying and dividing √2-√3

by using the algebraic identity,

(a+b)(a-b) = a²-b²

here a = √2, b = √3

$= \frac{ \sqrt{2} - \sqrt{3} }{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }$

$= \frac{ \sqrt{2} - \sqrt{3} }{2 - 3}$

$= \frac{ \sqrt{2} - \sqrt{3} }{ - 1}$

$= - ( \sqrt{2} - \sqrt{3} )$

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

Hope this is helpful❤