AI Tutor
If you see x+4=10\sqrt{x} + 4 = 10, your first instinct might be to square everything right away. But if you square both sides immediately, you do not get x+16=100x + 16 = 100.
Squaring a sum requires multiplying out a binomial: (x+4)2=x+8x+16(\sqrt{x} + 4)^2 = x + 8\sqrt{x} + 16. Squaring too early does not eliminate the root — it actually leaves you with a messier radical than you started with.
So how do we clear out the surrounding numbers so squaring actually works?

Isolating the Radical

An isolated radical is a square root expression that sits completely alone on one side of the equal sign, with no constants added, subtracted, or multiplied outside of it.
To isolate the root, treat the entire radical symbol like a single variable box and undo operations in reverse order: add or subtract outside constants first, then divide by any outside coefficients.
What does this step-by-step process look like in a full equation?

Worked Example: Constants and Coefficients

Let's solve 23x−2−4=82\sqrt{3x - 2} - 4 = 8. Before touching anything inside the root, we must get that square root alone on the left.
Always verify your answer in the original equation: 23(38/3)−2−4=238−2−4=2(6)−4=82\sqrt{3(38/3) - 2} - 4 = 2\sqrt{38 - 2} - 4 = 2(6) - 4 = 8, which confirms x=38/3x = 38/3 is correct.