How do you evaluate #\sqrt { 8+ \sqrt { 14+ \root[ 3] { 6+ \sqrt { 4} } } }#?

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Answer 1 · 2017-04-24T22:43:31

#2sqrt3#

Beginning from left to right

#root(3)(6+sqrt(4))=root(3)(6+2) = root(3)(2^3) = 2#

now

#sqrt(14+2)=sqrt(4^2)=4#

now

#sqrt(8+4)=sqrt(3 xx 2^2)=2sqrt3#

so finally

#\sqrt { 8+ \sqrt { 14+ \root[ 3] { 6+ \sqrt { 4} } } } = 2sqrt3#