Question

prove that

Answer 1

\[7^{\sqrt{5}}>5^{\sqrt{7}}\]

Answer 2

Calculate both sides. We know that \[7^{\sqrt 5} = 77.57051327...\]\[5^{\sqrt 7} = 70.68069404...\]Thus lead us to proof: \[77.57051327... > 70.68069404...\]

Answer 3

i forgot to say without calculator

Answer 4

Just said it next time. You know, we going to use calculator to show proof, lol.

Answer 5

number 2)\[\sqrt[3]{60},2+\sqrt[3]{7}\]wich one is larger ,you can help with this one

Answer 6

I think I remember seeing that second one before..

Answer 7

Had something to do with factoring and pulling apart terms.

Answer 8

i posted last time but no solution

Answer 9

inequality\[\frac{ x+y }{ 2 }<\sqrt{xy}\]

Answer 10

\[\frac{ x+y+z }{ 3 }<\sqrt[3]{xyz}\]
geometric mean

Answer 11

@TuringTest does that help

Answer 12

I don't know, I horrible at this kind of thing :P

Answer 13

http://openstudy.com/users/jonask#/updates/50892d42e4b05241909174da

Answer 14

i we can show that\[\frac{ 10+3+2 }{ 3 }\le \sqrt[3]{10*3*2}\]
\[5\le \sqrt[3]{60}\]
\[2+\sqrt[3]{7}<2+\sqrt[3]{8}=4\]
these proves that \[\sqrt[3]{60}\ge 2+\sqrt[3]{7}\]