Correct or wrong

Algebra Level 3

Which one of the following is correct?

A. p =√(25) ⇒ p = ± 5

B. p =√(25) ⇔ p = ± 5

C. p =√(25) ⇔ p = -5

D. p =√(25) ⇔ p = 5

A All are wrong C D B

1 solution

Md Zuhair
May 11, 2017

We know that

$|x|^2=x^2$

$\implies \sqrt{x^2}=\sqrt{|x|^2}$

$\implies |x| = \sqrt{x^2}$

$\implies |5| = \sqrt{5^2}=\sqrt{25} \implies |5| = 5$ (Ans)

(-5)²=25 -5=√(25)

Is that right?

I Gede Arya Raditya Parameswara - 4 years ago

No that isnt right....

This is because $\sqrt{25} =|(-5)| \implies 5$ [As Per Your Query] You wrote

$(-5)^2 = 25.$ Thats true but taking its square root is not -5,

Never as i said

$|x|^2=x^2$ ,

Isnt it correct??

Its always true..

$\sqrt{x^2}=|x|$ which is always +ve.

Thanks.

Md Zuhair - 4 years ago

$x^{2}=5$ so the value of $x$ just 5 or 5 and -5

I Gede Arya Raditya Parameswara - 4 years ago

Its $\sqrt {5}=x$ and $\sqrt {5}=-x$

Md Zuhair - 4 years ago