Why does 'x to the half power' mean square root?

Have you ever wondered why the "half power" means square root? Did someone just decide that's how it was going to be? In this video, we'll explain precisely and simply why the "half power" means square root!

[theguy]

You know that feeling, when you just can't get to the solution. But if you hear it you feel incredibly stupid.

[jonahconner]

I've wondering about why exactly this works...and no one explained it. Thank you for this video!

[xbdullah]

Great explanation, very easy to understand. Thank you so much and keep up the good work :)

[billylardner]

Concise, short, and well explained. Couldn’t ask for anything more. Thank you.

[AyushSingh-jsrf]

But from where 1/2 came! when it was discovered does they tested it with various values 😶

It's a Great Explanation and Proving

But still that doesn't defined the reason why?

Title should be proof of 1/2 = Square Root.

[DezeereaM]

This video did not explain WHY x to the (1/2) power = sq root of 2. This left me just as confused as I was before watching the video.

[Stickia]

I was doing school but got stuck on a question, and this video help me understand why x to the 1/2 power is the same as square root.

[avjotmiglani]

Best video ever.Thank you so much sir for making students understand the problems that no teacher ever gives them the reasoning for.You have really aided many .May god bless you.

[itengineeremmanuel]

I've just start watching your content and I guess that how some teachers should explain math, with logic, not just with formulas. Thanks

[funfeces]

how would you write it out? ex:3^2 written out is 3*3 so what would 9^1/2 be written as?

[theobserver]

Alternatively, you can draw a square of equal side lengths and prove why Square roots work.

[daltonmatthews]

me working on a physics lab in college trying to find the sciency term for a radical relationship :(

[bloodsword]

your explanation is the best so simple and the words can't explain your great job
You deserve a subscribe

[Orblitz]

the problem with this is that it assumes you already have the exponent formulas. It would be better if you showed why it worked without them

[SebastienPatriote]

I've got a question. Using the fact that we know a^b^c=a^(b*c), and that sqr(2)=2^(1/2), we can take any number, lets use e since it's easy to do powers with it and we have:

e^(sqr(2))=e^2^1/2, leading to e^(sqr(2))=e^(2*1/2) which means:

e^(sqr2)=e^1. If we take the natural log on each side we get sqr(2)=1, which is oubviously wrong. So where did I make my mistake??

[alishbarafi]

I have a question that why are we doing (3²)½ and (9)½?

[sampadajoshi]

Let's say we do not know that answer is y so how do we go about calculating x to the power of 1/2?

[thejayantjadon]

No one explained it.. Thank you for this video

[frorgnx]

Sir If u make kind of like strategy video to solve aljebra equations so that would be incredibly beneficial

[MFfp]

Thank you so much! I appreciate you helping us to fully understand!