1Cademy - Simplifying $$2\sqrt{2}

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Adding and Subtracting Like Square Roots
Adding and Subtracting Like Radicals

Example

Simplifying $2\sqrt{2} - 7\sqrt{2}$

To simplify $2\sqrt{2} - 7\sqrt{2}$ , recognize that both terms share the identical radicand $2$ and are therefore like square roots. You can combine them by subtracting their coefficients, exactly as you would with algebraic like terms. Compute $2 - 7 = -5$ , and keep the radical unchanged to get $-5\sqrt{2}$ . This illustrates how subtracting a larger coefficient from a smaller one results in a negative coefficient, just as $2x - 7x = -5x$ .