This is sometimes true; it is only true for a=1 or a=0.
We can combine radicals much as we do variables:
[tex]\sqrt{a}+\sqrt{a}=2a
\\
\\2\sqrt{a}=2a[/tex]
Divide both sides by 2:
[tex]\frac{2\sqrt{a}}{2}=\frac{2a}{2}
\\
\\\sqrt{a}=a[/tex]
We can cancel the square root by squaring both sides:
[tex](\sqrt{a})^2=a^2
\\
\\a=a^2[/tex]
Now we can divide by a:
[tex]\frac{a}{a}=\frac{a^2}{a}
\\
\\1=a[/tex]
However, if we use a=0 this also works.