## Akshit_math 3 years ago The value of _____

1. hartnn

is _______

2. Akshit_math

$\sqrt{1 + 2008\sqrt{1 + 2009\sqrt{1 + 2010\sqrt{1 + 2011.2013}}}}$

3. Akshit_math

what is the value of the above ???

4. Mimi_x3

do you have access to a calculator? or do you want to solve it by hand?

5. Akshit_math

we are Indians and here most of the time its by hand ...so please try to solve and help me out without the use of calculator,,

6. hartnn

ok, now can u write 2011*2013 as (2012-1)(2012+1) ?? and do u know what (a+b)(a-b) =??

7. Akshit_math

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

8. hartnn

good, so what will be (2012-1)(2012+1) =??

9. Akshit_math

$2012^{2}-1$

10. hartnn

and u had 1+ 2011*2013 so now whats 1+2012^2-1 ??

11. Akshit_math

heyyyyy thaaaanzzznnzzzz buddy i got it all after dat ...u made it so easy 4 me now!!!...champ!!!..thnak u!

12. hartnn

welcome :)

13. Akshit_math

hey @sriramkumar u typing since long tym eh!

14. sriramkumar

let 2012=a, then the problemn becomes $\sqrt{1+(a-4)\sqrt{1+(a-3)\sqrt{1+(a-2)\sqrt{1+(a-1)(a+1)}}}}$ then the inner root becomes $a ^{2}-1 +1=a ^{2}$ $1+(a-2)\sqrt{a ^{2}}=1+(a-2)a=1+a ^{2}-2a=(a-1)^{2}$ ...... and so on....

15. Akshit_math

damn gud!!!....@sriramkumar

16. Akshit_math