Question

Rationalize the denominator:- 1 + √2 ÷ 2 - √2

Answer 1

Answer:

\large\bold\red{\frac{4+3\sqrt{2}}{2}}

Step-by-step explanation:

Given,

\frac{1 +  \sqrt{2} }{2 -  \sqrt{2} }  

Rationalisation of Denominator

=  \frac{(1 +  \sqrt{2)} }{(2 -  \sqrt{2}) }  \times  \frac{(2 +  \sqrt{2} )}{(2 +  \sqrt{2}) }  \\  \\  

Now,

we know that,

(x + y)(x - y) =  {x }^{2}  -  {y}^{2}  

Therefore,

we get,

=  \frac{(1 +   \sqrt{2} )(2 +  \sqrt{2} )}{ {(2)}^{2} -  {( \sqrt{2}) }^{2}  }   \\  \\  =  \frac{2 +  \sqrt{2} + 2 \sqrt{2}   + 2}{4 - 2}  \\  \\  =  \frac{4 + 3 \sqrt{2} }{2}  

Hence,

Denominator is rationalised.

Step-by-step explanation:

Answer 2

= 1+√2/2-√2 × 2+√2/2+√2

= 2(1+√2 ) + √2(1+√2) / (2)^2 - (√2)^2

= 2+2√2 + √2+2 /4-2

= 4+3√2/ 2