square roots

pls help:

someone out there, pls help me... this is my 4th post:

what is the square root of 392, is it an irrational number?

19 ²= 361
20 ²=400

so sqrt(392) is an irrational number.

392 divided by 4 = 98
98 divided by 49 = 2
so
4 x 49 x 2 = 392
sqrt(392) = 2*7* sqrt(2) = 14sqrt(2)

Thank you very much... I can finaly finish my homework after being online searching for the answer for about 4 hours(sigh)

Thank God~~~~~~~~~~

Thank you very much... I can finaly finish my homework after being online searching for the answer for about 4 hours(sigh)

Thank God~~~~~~~~~~

grateful person:

Thank you very much... I can finaly finish my homework after being online searching for the answer for about 4 hours(sigh)

Thank God~~~~~~~~~~

No one has ever called me God before. Sounds a bit irreligious.
(I hope no one is offended)

lol, thanks anyway, no offence to religious people around the world

Of course, we could just plug 392 into a calculator to see what we would get.......but let's not!!

Let's break this down into some factors and see what happens.

Since it's even, it's divisible by 2, so it factors as 196 *2

But 196 is even as well, so we can divide it by 2, and 392 factors now as 196*2 = 98*2*2 = 98*4

But 98 is divisible by 2 so we get 98*4 = 49*2*4 = 49*4*2

So.....SQRT(98) = SQRT(49*4*2)

Note that SQRT(49*4*2) can be written as SQRT(49) * SQRT(4) * SQRT(2)

And SQRT (49) =7 And SQRT(4)=2

But SQRT(2) is irrational (I can't do anything with it!!)

So, if we factor any positive integer under a square root and end up with any part of it being irrational, then the whole thing was irrational to begin with - i.e., the SQRT(392) is an irrational quantity!!

TQ to both melody and CPhill for ur replies