Spain | A Nice Square Root Algebra Problem | Math Olympiad

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[@عبدالواسع-س8م]

Well done ! Thanks so much !

[@AmirgabYT2185]

5(√3+√2)

[@yurenchu]

√( 25/(5 - √24) ) =
= 5 * √( 1 / (5 - √24) )
= 5 *√( (5 + √24) / [(5 - √24)(5 + √24)] )
= 5 * √( (5 + √24) / [ 25 - 24 ] )
= 5 * √( 5 + √24 )
= 5 * √( 5 + 2√6 )
= 5 * √( 3 + 2 + 2√(3*2) )
= 5 * √( (√3 + √2)² )
= 5 * (√3 + √2)
= 5√3 + 5√2