That's ab-surd!

Algebra Level 4

Which is equal to $\sqrt {x^{ 2 } }$ ?

{ (\sqrt { -x } ) }^{ 2 }

x

\pm x

abs(x)

-x

1 solution

Abdur Rehman Zahid
Feb 4, 2015

$\sqrt{x^2}$ is designated to be equal to $|x|$ which can be written as $abs(x)$

Highly over-rated!!

Nihar Mahajan - 6 years, 2 months ago

How come that $\sqrt(-x)^{2}$ is wrong $\sqrt (-x)^{2} = abs(-x) = abs(-1)*abs(x) = abs(x)$

Paul Ryan Longhas - 6 years, 4 months ago

Note that, $\exists x\mid \sqrt{(-x)^2}\neq (\sqrt{-x})^2$

And that is the reason the option $(\sqrt{-x})^2$ is incorrect! You can easily observe that $x=5$ is a counterexample to that option.

Prasun Biswas - 6 years, 4 months ago

Thanks for clearing my concept :D

Paul Ryan Longhas - 6 years, 4 months ago

@Paul Ryan Longhas – Mention not. :)

Prasun Biswas - 6 years, 4 months ago