Multistep Equation with Square Root Confusion

Question

Alright, so I have $4 * \sqrt{3} = \sqrt{x}$ So I squared the entire equation to get $$16 * 3 = x$$ $$x = 48$$ Is this correct? Or do I only square the $\sqrt{3}$ part on the left side of the equation?

Answer 1

If you do something to one side of the equation you have to do it to the other. You are correct to square the entire left hand side.

$$a\sqrt{b} = \sqrt{x}$$ $$ (a\sqrt{b})^2 = (\sqrt{x})^2$$ $$ a^2b = x$$

Answer 2

You can easily check, of course - what is the square root of $48$? But that is simply retracing your steps through your solution.

But essentially, you were correct - squaring both sides of the equation should give another valid equation, but squaring only one term will generally not.