Question

for all non negative real number a and b ,√ab=√a√b​

Answer 1

Step-by-step explanation:

Yes unless both a and b both negative. Apart from this exception, this property can be used everywhere , even in the complex field.

Let us take an example...

√2*√2=√(2*2)=2;::::: in this case there is no problem as both a and b are both positive.

Let us take another example.

√2*√-2=√2*√2*i=2i......

√(2*-2)=√-4=2i(again)

: in this case again,there is no problem as both a and b are not negative.

Let us see another example which contradicts what we have seen so far.

√-2*√-2=√2*i*√2*i=-2......

√(-2*-2)=√4=2

Clearly it is not the same.