Filling the gap in knowledge of algebra

Question

Recently, I realize that my inability to solve problems, sometimes, is because I have gaps in my knowldge of algebra. For example, I recently posted a question that asked why $\sqrt{(9x^2)}$ was not $3x$ which to me was fairly embarrassing because the answer was fairly logical and something that I had missed. Furthermore, I realize that when I am solving questions, I tend to get stuck on some intermediate step because that is where most of the algebra is needed. Therefore, my question is: How can I improve algebra? What steps are needed? What books should I be practicing from? What are a few things everyone should know?

Answer 1

As skullpatrol commented, the Khan Academy has covered a wide range of high school algebra. As you go up the scale, there are many more resources such as the Art of Problem Solving for contest mathematics. Art of Problem Solving has books on high school algebra as well as practice problems: I personally like their structure. You can use your mathematics textbooks for algebra too. Another website I want to add is Brilliant.

P.S.: Never forget the site you are already on! Set the algebra-precalculus tag as your favorite and start exploring.

Answer 2

For the first year course (in maths) at my University they recommend "Basic Linear Algebra" by Blyth and Robertson and "Algebra" by Michael Artin. The first book is probably more what you're looking for.

EDIT: Just to expand, the "Basic Linear Algebra" book would cover things like why $\sqrt{9x^2} = 3x$ isn't always simply the case from very early on in the book. It is mostly "basic" linear algebra like the name suggests but it's a good read to more rigorously understand algebra.