Basic calculation with root roots and power Sorry for the boring question but I just need someone to remind me the way to calculate this:
$\displaystyle \left(\frac{a}{2}\right)^2 + x^2 = a^2$ (i used carrot sign cause i dont know how to do factorial in my mac keyboard)
The answer is $\displaystyle \frac{\sqrt {3}}{2}a$ but i forgot how to calculate this type of exercise, can someone be kind enough and help? 
tnx

$$\left(\frac a2\right)^2=\frac{a^2}{2^2}=\frac{a^2}4.$$ Thus, using the difference of squares identity $$y^2-z^2=(y-z)(y+z),$$ the following are equivalent: $$\left(\frac a2\right)^2+x^2=a^2\\x^2+\frac{a^2}4-a^2=0\\x^2-\frac{3a^2}4=0\\x^2-\left(\frac{a\sqrt{3}}2\right)^2=0\\\left(x-\frac{a\sqrt{3}}2\right)\left(x+\frac{a\sqrt{3}}2\right)=0.$$ Now what can you conclude from that? (Incidentally, the answer you mention is incorrect.)
