Nice Square Root Math Simplification | How to Solve !!! |Olympiad

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...= 464.758

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√(30³ + 40³ + 50³)
√{( 3× 10)³ + ( 4 × 10 )³ + ( 5 × 10 )³}
√ 3³ × 10³ + 4³ × 10³ + 5³ × 10³ { (ab)³ = a³ × b³ }
√ 10³( 3³ + 4³ + 5³)
√10³× (27 + 64 + 125 )
√10³ × 216
√ 10³ × 6³
√ 60³ { a³ × b³ = ( ab)³ }
√ ( 60² × 60¹) [ a^m × a^n = a^m+n { ^ = raised to the power } ]
√60² × √60 { √ab = √a × √b }
60 × √60 = 60√60
60√60 = 60√(4 × 15)
= 60 × √4 × √15 { √ab = √a × √b }
= 60 × 2 × √15
= 120√15 ✅✅✅✅