Isolate, then square
SAT glossary · Course Foundations
Definition
The mandatory first move on any radical equation: never square a sum containing a radical. Squaring √(x+5)+3=x directly produces x+5+6√(x+5)+9 — the radical survives and the problem is worse.
Isolate, then square in plain English
When you're solving an equation that has a square root in it, like √(x+5)+3=x, your very first move must be to get the square root term completely ALONE on one side before you square anything — never square a sum that still has a radical mixed into it. If you try to square the whole left side as-is, you get a mess: (√(x+5)+3)^2 = x+5+6√(x+5)+9 — notice the square root is STILL sitting there, just wrapped in more stuff, meaning you accomplished nothing and made the problem harder. Isolating the radical first (moving the 3 away) means that when you square, the root actually disappears for good.
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