Let's Compare Two Numbers

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[@abdesselambassou3618]

Hi. I suggest to compare 10xlog(2) and 3.
You do a great work, continue👏

[@MniDaIlM]

How would you do that?

[@stvp68]

Yay, radicals!!!!!!

[@forcelifeforce]

*@ SyberMath Shorts* -- You are leaving out the most standard, direct method, and it does not use any approximating:
Sqrt[5 + 5sqrt(5)] vs. 4
{Sqrt[5 + 5sqrt(5)]}^2 vs. (4)^2
5 + 5sqrt(5) vs. 16
5sqrt(5) vs. 11
[5sqrt(5)]^2 vs. (11)^2
25(5) vs. 121
125 > 121
Therefore, sqrt[5 + 5sqrt(5)] *>* 4.

[@mystychief]

That's what I had. Squaring is possible without changing which side is bigger because both are positive.

[@maxhagenauer24]

Are you sure you can just apply it like an algebraic equation and do whatever you want as long as you do it to both? Its not an equation of any sort.

[@robertveith6383]

​@@maxhagenauer24 -- The same operations are done to each side, and note the comment from the first reply about squaring.

[@maxhagenauer24]

@@robertveith6383 I know but if you square something less than 1 like 1/2 then you get something smaller but if you squares something bigger than 1 then it becomes bigger. Are you sure you can square both sides like that ehen comparing any 2 numbers and the bigger vs smaller of the numbers still hold true?

[@robertveith6383]

​@@maxhagenauer24 -- Every quantity on each side in every step happens to be greater than 1. It is not the situation here, but had an expression been positive between 0 and 1, and it got squared, that would have been okay. What would not have been okay is if in adding or subtracting quantities from each side, that at least one side had become negative, then squaring afterward would not be legitimate.

[@BorisRaifler]

If we square both sides we'll get 5 + 5*sqrt(5) vs. 16. Substract 5 from both sides we'll get 5*sqrt(5) vs. 11. Square once more both sides we'll get 125 vs. 121 -> 125 > 121, therefore LHS > RHS

[@Skank_and_Gutterboy]

This is what I did:
Suppose that √(5+5√5) > 4. Then:
5+5√5 > 16
5√5 > 11 ( Note that 5(2.2) = 11, so 11/5 = 2.2 )
√5 > 2.2
5 > 2.2^2 (This is very easy to hand-multiply, 2.2 x 2.2 = 4.84)
5 > 4.84
Because 5 > 4.84 is true, all steps above are true and √(5+5√5) > 4 QED.

[@DonEnsley-mathdrum]

Assume
√(5+5√5)

[@DonEnsley-mathdrum]

@@robertveith6383 see edited comment. 🙏 thx

[@Qermaq]

My approach was to square both sides, so 5 + 5sqrt(5) relates to 16. Then I can subtract 5 from both sides, so 5sqrt(5) relates to 11. Then I square both sides again, so 125 relates to 121. As I have done nothing to upset the inequality, since 125>121, sqrt(5 + 5sqrt(5)) > 4. And maybe others posted that they did it the same way. It doesn't matter. I'm sharing with the community. That's what this is all about.

[@robertveith6383]

Your *duplicate* solution is redundant, so therefore it is *spam,* and it is reported as such. Come up with a *unique* method for a solution when you bother to post in the forums instead of trying to get noticed for what another forum user already achieved and beat you to it. (Edit.) And, it got reported again today as persistent spam that it is.