# Thread: Solving equations with roots

1. ## Solving equations with roots

Ok, how would I go about solving the following equation with algebra?

a + a^(1/2) = 20

OR: a plus the square root of a equals 20.

I can't seem to work out how you do it. I know that the answer in this case is a = 16, but I'm not sure how you would arrive there with algebra. Any help would be appreciated.

2. Hello,
Originally Posted by Wowsa
Ok, how would I go about solving the following equation with algebra?

a + a^(1/2) = 20

OR: a plus the square root of a equals 20.

I can't seem to work out how you do it. I know that the answer in this case is a = 16, but I'm not sure how you would arrive there with algebra. Any help would be appreciated.
substitute $\displaystyle b=a^{1/2}$
note that $\displaystyle a=(a^{1/2})^2=b^2$

so you're in front of a quadratic get the values for b and keep the positive ones

3. Originally Posted by Moo

so you're in front of a quadratic get the values for b and keep the positive ones
Could you explain that bit to me in more detail please? I'm a bit of a newb at algebra and I'm not sure I understand what you did.

4. I've worked out what you meant now, thanks for your help.