Question

Are the following function equal-
(√x)^2. And. (x^2)^1/2

Answer 1

I think not

Answer 2

lets check,

\(\sqrt x = x^{1/2}\)

so 1st one is
\(x^{(1/2) \times 2} = x \)

Answer 3

Because I can't plug -1 in first
But can plug in second function

Answer 4

the second one is \(x^{(2 \times (1/2))} = x\)

and both will always give out positive answers.
so i don't see any difference

Answer 5

This is not true for any negative integer

Answer 6

Also the domain of both function are not same

Answer 7

Which is a necessary condition for two function to be equal.

Answer 8

yes, thats correct,

since we are applying the square root function first,
for the domain to be real,
x should be >=0.

you're right, tested with -4,
the first one gives -4, the 2nd one will give 4

Answer 9

Yea...

Answer 10

The first function don't accept -4 or any negative number

Answer 11

\((\sqrt{-4})^2 = (2\sqrt{-1})^2 = (2i)^2 = 4i^2 = -4\)

Answer 12

\(((-4)^2)^{1/2} = 16^{1/2} = (4^2)^{1/2}=4\)

Answer 13

But -4 is not in domain of √x
But I think we don't considered I much in algebra

Answer 14

good point, so they don't even match at domain level

Answer 15

iota ...I mean

Answer 16

-4 is not in the real domain,
if we can consider imaginary numbers, then -4 it is.