Question

what is the value of 6^1/8 ?

Answer 1

1.251033405 is the answer

Answer 2

$\sqrt[8]{6}=1.2510334048590738236780437177798$
without calculator
take log
$log_{10} 6^{ \frac{1}{8} }= \frac{log_{10} 6}{8}= \frac{0.7781}{8}= 0.0973$
$\sqrt[8]{6}= 10^{0.0973}=1.2510334048590738236780437177798$
ANOTHER METHOD(Trial and error)
$1^{8}=8,2^{8}=256$
so ur answer must lie between 1 and 2
and it must be close
$1.5^{8}=\frac{3^{8}}{2^{8}}= \frac{6561}{256}=25.63$
then go for
$1.1^{8}= \frac{11^{8}}{10^8}=2.14*10^{-8}$
very less
then go for 1.2
$1.2^8= \frac{6^8}{5^8}= \frac{1679616}{390625}=4.2$
little less
so it is between 1.2 to 1.3
1.25 mean