Question

Is this true? Why?

Answer 1

Is what true?

Answer 2

\[\Large \sqrt{a^2} = (\sqrt{a})^2\]

Answer 3

true :)

Answer 4

And why?

Answer 5

for example:
\[\sqrt{9} = 3 = (\sqrt{9})^{2}\]

Answer 6

Both sides are equal, that's why it's true.

Answer 7

Are you guys sure? xD

Answer 8

enothing is %100 ! :D

Answer 9

\(\sqrt{4^2} = \sqrt{16}=4\)
\((\sqrt{4})^2=4\)

Answer 10

What if we take -4? @austinL

Answer 11

\[\pm \sqrt{x}\]

Answer 12

notm\[\not +\sqrt{x} \]

Answer 13

it's not true - for -4 you get 4 and 4i

Answer 14

\(\sqrt{(-4)^2}=\sqrt{16}=4\)
\((\sqrt{(-4)})^2=-4\)
It doesn't necessarily hold true in all instances.

Answer 15

no, *-4

Answer 16

but @austinL I think the second one is false!

Answer 17

how about taking x=4i?

Answer 18

But, the square would remove the square root first before you evaluate the root.
\(((-4)^{\frac{1}{2}})^2=-4\)

Answer 19

yes,so it is false :D

Answer 20

Exactly, so if one instance breaks the statement, then you must hold it false.
How could we make this true? ;)

Answer 21

I will say this to my teacher,Thank you :) :D

Answer 22

guys guys take x=4i :3