1Cademy - Simplifying $$4\sqrt{x}

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Adding and Subtracting Like Square Roots

Example

Simplifying $4\sqrt{x} - 2\sqrt{y}$

Simplify the expression $4\sqrt{x} - 2\sqrt{y}$ , which contains two square roots with different radicands.

The first term has radicand $x$ and the second has radicand $y$ . Because the radicands are not the same, these are not like square roots. Their coefficients cannot be combined — the expression is already in its simplest form.

$4\sqrt{x} - 2\sqrt{y} = 4\sqrt{x} - 2\sqrt{y}$

This is analogous to the algebraic expression $4x - 2y$ , which cannot be simplified further because $x$ and $y$ are different variables. Attempting to subtract unlike square roots would be an error, just as attempting to combine unlike terms would be.