@@yurenchu what I intended to arrived was a quick and mistakenly wrote. To clarify it should have been as follows: 6 √(6 +√ 35) √6.√(36 +6√35) √6 √(√21 +√15) ^2 √6(√21 +√15) Thanks for pinpointing the same.
What do you mean? Did you derive the answer as (6√6)/(√21 - √15) , with an non-reduced denominator? (Note that both numerator and denominator also contain a factor √3 , so the numerator and the denominator aren't even in co-prime terms.)
Thank you this is very helpful!
Excellent ! Thank you so much !
sqrt (36) has 2 roots: +6 and -6.
3(√14 + √10)=20.712
√14 + √10 = 6.904x3=20.712
√( 36/(6 - √35) ) =
... multiply both numerator and denominator within square root operator by (6+√35) ...
= √( 36(6+√35) / [(6 - √35)(6+√35)] )
= √( 36(6+√35) / [(36 - 35)] )
= √( 36(6+√35) / [1] )
= √( 9*4*(6+√35) )
= √( 9*(24+4√35) )
= √( 9*(24+2√140) )
= √( 9*( 14 + 10 +2(√14)(√10) ) )
= √( 3²*(√14 + √10)² )
= 3*(√14 + √10)
= 3√14 + 3√10
@@yurenchu what I intended to arrived was a quick and mistakenly wrote. To clarify it should have been as follows: 6 √(6 +√ 35)
√6.√(36 +6√35)
√6 √(√21 +√15) ^2
√6(√21 +√15)
Thanks for pinpointing the same.
Interesting surd puzzle which ends with ( √21 - √15 )
What do you mean? Did you derive the answer as (6√6)/(√21 - √15) , with an non-reduced denominator? (Note that both numerator and denominator also contain a factor √3 , so the numerator and the denominator aren't even in co-prime terms.)