How do you solve x squared equals 12?

Answer 1

You take the square root on both sides of the equation. In general, when taking square roots, you need to put a "plus/minus" sign just right of the equal sign; otherwise, you may lose solutions.

Therefore to solve x2=12

x= √12 or -x=√12

The question then becomes how to find the √12

The simple and modern answer i sto simply push the SQRT or √ button on your calculator to find √12= 3.4641. A book of Logarithmic Tables gives the same answer.

If you've no book of tables and the calculator is dead you can do the equation longhand or by graphical or "by guess and golly" estimation.

In the last method you know that √9=3 and the √16=4 so the√12 is somewhere in between. You multiply 3.5 by itself to get 12.25 so you know the √12 is a bit less than 3.5. You try again with slightly maller number and range in by iteration.

Graphically the method is the same except you plot your answers on a graph of x vs x2.

The most exact manual method is shown at the link.