is my working correct? i need to find which number is bigger. i concluded that 2*sqrt38 is bigger of the two since 38^2 = 1444

Question

anonymous · Answer

attched is my working

anonymous · Answer

seems correct

anonymous · Answer

thanks a lot!

anonymous · Answer

(:

asnaseer · Answer

yes - correct again.

BTW: you can make use of this fact:$$a^2\gt a^2-1$$$$\therefore a^2\gt (a+1)(a-1)$$In this case a=38 so you know that:$$38^2\gt (38+1)(38-1)$$

anonymous · Answer

how did you just decide a = 38? @asnaseer

asnaseer · Answer

in your last step you had:$$38^2?39\times37$$

asnaseer · Answer

so can conclude ? is ">" without actually evaluating $38^2$

anonymous · Answer

but 38^2 is "a" but 39 x 37 is not = (a+1)(a-1) so how can you compare that way?

asnaseer · Answer

no, a=38, remember the identity I showed was:$$a^2\gt (a+1)(a-1)$$so, if a=38 we get:$$38^2\gt(38+1)(38-1)$$$$\therefore 38^2\gt39\times37$$

anonymous · Answer

wow!! i see it now. where did you know this. 

i never came across this before?

asnaseer · Answer

nor did I - I just suddenly "spotted" the pattern - that is one of the beauty of maths, you never know what subtleties you will discover. :)

anonymous · Answer

thanks...

asnaseer · Answer

yw :)