Rules for addition / division etc for Square roots.

[peblez]

Hello. I can't find this on any websites. I'm basically in need of rules that govern how square roots work. For example:

Is this the same? sqrt(a) + sqrt(b) = sqrt ( a + b) ? or are they seperate

Sqrt ( a ) x sqrt ( b) = sqrt ( a x b) ?? is this correct?

sqrt ( a ) / sqrt ( b ) = sqrt ( a / b) ?? is this true>?

 

[arthur ohlsten]

does the square root of a + square root b=square root [a+b] ?
sqrtA+sqrtB=sqrt[A+B] ?

as a test let A=16 and B=25
sqrt16+sqrt25=?sqrt[16+25]
4+5=?sqrt[41] no!

proof
square both sides
sqrtA+sqrtB=?sqrt[A+B]
A +2sqrtAsqrtB +B=?A+B
subtract A and subtract B FROM BOTH SIDES
2 sqrtA sqrtB =?0
only if A or B =0

===================================================

sqrtA sqrtB=?sqrt[AB] square both sides
AB =? AB yes

===================================================
sqrt A / sqrtB =? sqrt[A/B]
a simple test
let A=36 and B= 9
sqrt36/sqrt9 =? sqrt [36/9]
6/3=? sqrt 4
2=?2 yes then probably true

sqrtA / sqrtB =? sqrt[A/B]
sqrtA =? sqrtB sqrt[A/B]
square both sides
A=? Bx[A/B]
A=?A yes

Arthur