Japan | A Nice Olympiads Trick | No Calculator Allowed

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[@evlorenzoni]

No simplification at ALL 😂

[@hls6925]

Your problem is introduced on the initial KZbin screen (URL: kzbin.info/www/bejne/apXHl32ropufb9E), as (2/5)^2/5, NOT as (5/2)^2/5. You need to correct this. Incidentally, using a spreadsheet, one can quickly calculate that the fifth root of 200, divided by 2, i.e. (200^1/5)/2 = 1.4427 (to 4 dp)

[@icheichigo]

you just rationalize the denominator. And calculate nothing!

[@johnstanley5692]

This is not a trick its more of an hindrance. If calculator is not allowed then only option is use Taylor expansion to get an approximation. e.g. express 25/4 = 32*(1-x)/(1+x) . here x=103/153. (25/4) ^(1/5) is approximated 2*(- (18*x^3)/125 + (2*x^2)/25 - (2*x)/5 + 1) ~ 1.4461. Even this method is tedious. Better option is use calculator or any mobile phone to compute (25/4)^(1/5)

[@RyanLewis-Johnson-wq6xs]

(5/2)^(2/5)=0.5Surd[200,5]