Quesiton about radicals

[samalex]

Hi,

I'm working through a homework assignment to solve for x^2+2x=12, and the instructions say to use radicals as needed.

My factoring is as such:
x^2+2x-12=0
then I used quadratic equation to get this:
-1 ± sqrt(52)/2
-1 - sqrt(52)/2 , -1 + sqrt(52)/2

It said this answer was equal to the correct answer but to read the question better to put it in the correct format. After I had no clue it said the correct answer is :

-1 ± sqrt(13)
-1 - sqrt(13) , -1 + sqrt(13)

So how does sqrt(52)/2 equal sqrt(13) ? When I put these two values into the calculator they do equal, but how do I convert the first to the latter?

Thanks for any advice on this,

Sam

 

[soroban]

Hello, samalex!

\(\displaystyle \text{How does }\frac{\sqrt{52}}{2}\text{ equal }\sqrt{13}\;?\)

Simplify the radical:

. . \(\displaystyle \displaystyle \frac{\sqrt{52}}{2} \;=\;\frac{\sqrt{4\cdot13}}{2} \;=\;\frac{\sqrt{4}\cdot\sqrt{13}}{2} \;=\;\frac{2\cdot\sqrt{13}}{2} \;=\;\sqrt{13}\)