Question

Why is this not true...?

Answer 1

\[\sqrt{(\ln2)^2 +1} = \ln2 +1\]

Answer 2

because powers (and hence roots) do not distribute to addition

Answer 3

for the same reason that
\[\sqrt{3^2+4^2}\neq 3+4\]

Answer 4

in fact it must be the case that
\[\sqrt{a^2+b^2}<a+b\] by the triangle inequality, unless of course one of them is zero

Answer 5

is this true? \[\sqrt{(\ln2)^2 +1} =( \ln(2) +1)^{1/2}\]

Answer 6

yes it is.

Answer 7

then is this true? \[(\ln(2)+1)^{1/2} = (\ln(2))^{1/2} + 1^{1/2}\]

Answer 8

you missed the square of ln 2

Answer 9

no. again, powers DO NOT distribute to addition.
it DOES distribute to multiplication:
\[ \large (ab)^n=a^n\cdot b^n \]

Answer 10

@helder_edwin thank you

Answer 11

[(ln2)^2 +1]^1/2

Answer 12

u r welcome

Answer 13

dont think you can reduced them any more...[(ln2)^2 +1]^1/2