Question

e) Simplify
i) 1/
1+root 2

ii)7+root3/7-root3​

Answer 1

Answer:

i>-1+$\sqrt{2}$

ii>52+14$\sqrt{3}$/46

Step-by-step explanation:

this question can be simplified by using the rationalize method-

which is 1/a-b=1/a-b*<a+b/a+b>

so the answer goes like this

i>     1/1+root 2

   = 1/1+root 2 *1-root 2/1-root 2

on dividing we get in numerator 1-$\sqrt{2}$ and in denominator we get =(1+$\sqrt{2}$)(1-$\sqrt{2}$)

1-2=-1                                      <(a+b)(a-b)=$a^{2}$-$b^{2}$>

so the final answer is = -1+$\sqrt{2}$

ii)7+root3/7-root3

7+root3/7-root3    

so by rationalization we get -

7+root3/7-root3    *    7+root3/7+root3

7+$\sqrt{3}$ whole square/     49-3    =   49+ 3+14$\sqrt{3}$/46

= 52+14$\sqrt{3}$/46

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thank buddy,

ADITYA PRIYADARSHI