Question 204020
this is where it gets confusing:
{{{(8 +- sqrt(124))/10}}}
The next step is simplifying the square root. Simplifying square roots is done by finding perfect square factors of the radicand (the number inside the square root), if possible. The largest perfect square factor in 124 is 4. So we can rewrite 124 as 4*31:
{{{(8 +- sqrt(4*31))/10}}}
Then we can use a property of square roots, {{{sqrt(a*b) = sqrt(a)*sqrt(b)}}}, to split apart the two factors:
{{{(8 +- sqrt(4)*sqrt(31))/10}}}
Now we can simplify square root of the perfect square:
{{{(8 +- 2*sqrt(31))/10}}}
The only thing left to do is reduce the fraction. This is done, as always, by finding common factors which will cancel. In this case 2 is a factor of both the numerator and denominator. So if we factor it out we can cancel them:
{{{(2(4 +- sqrt(31)))/(2*5)}}}
Now the 2's cancel leaving:
{{{(4 +- sqrt(31))/5}}}