a is a real number.
Demonstrate the following equality.
$\displaystyle \surd(a^2) = |a|$
I tried in this way but i think it is wrong.
$\displaystyle \surd(a^2) = a~~~(a\geq0)$
$\displaystyle a\geq0~~so~~a = |a|$
Is it correct?
a is a real number.
Demonstrate the following equality.
$\displaystyle \surd(a^2) = |a|$
I tried in this way but i think it is wrong.
$\displaystyle \surd(a^2) = a~~~(a\geq0)$
$\displaystyle a\geq0~~so~~a = |a|$
Is it correct?
You considered only the case $\displaystyle a\ge 0$. Also, since the problem is so basic, the proof has to be really detailed, and I am not sure you sufficiently explained why $\displaystyle \sqrt{a^2}=a$ when $\displaystyle a\ge 0$. So, what happen when $\displaystyle a < 0$? Recall that by definition $\displaystyle \sqrt{x}$ is a nonnegative number $\displaystyle y$ such that $\displaystyle y^2=x$.