how do i simplify the square root of 404?

Question

katherinesmith · Answer

like how do i break it down to a simpler square root

tkhunny · Answer

You must acquaint yourself with the idea of the "Prime Factorization".  Ever hear of it?

katherinesmith · Answer

somewhat

tkhunny · Answer

Fair enough.  Take 404 and find ANY factor.  Name one.

katherinesmith · Answer

2

tkhunny · Answer

404 = 2*202

Is 2 prime?
Is 202 prime?

katherinesmith · Answer

no, that can be divided by 2, and then you get 101

katherinesmith · Answer

which i think is prime

tkhunny · Answer

404 = 2*2*101

Are you SURE 101 is prime?

katherinesmith · Answer

yeah

tkhunny · Answer

The we're almost done: $\sqrt{404} = \sqrt{2*2*101} = \sqrt{2^{2}\cdot 101} = \sqrt{2^{2}}\cdot \sqrt{101}$

One more step.  Do you see it?

katherinesmith · Answer

the square root of 4 times 101

katherinesmith · Answer

so 2 to the square root of 101

tkhunny · Answer

Why did you go back to 4?  We found the prime factors so we wouldn't have to say that any more.

$\sqrt{2^{2}}\cdot\sqrt{101} = 2\sqrt{101}$

No more 4.  :-)

tkhunny · Answer

You beat me to it.  Excellent work.

tkhunny · Answer

It is hoped that you do NOT think of 4 when simplifying $\sqrt{2^{2}}$.  It's just 2.  No need to go through 4.

katherinesmith · Answer

okay. i hate this stuff. it's too much thinking.

tkhunny · Answer

It will be your friend, one day.  It will save you at a car dealer or when your kids are in high school.  One day, you will appreciate at least some small part.

Good work and good luck.