1Cademy - Simplifying $$5\sqrt{13} + 4\sqrt{13} + 2\sqrt{13}$$

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Adding and Subtracting Like Square Roots

Example

Simplifying $5\sqrt{13} + 4\sqrt{13} + 2\sqrt{13}$

Simplify the expression $5\sqrt{13} + 4\sqrt{13} + 2\sqrt{13}$ , which involves adding three like square roots.

All three terms contain the radical $\sqrt{13}$ , so they are all like square roots. Add the three coefficients while keeping the radical part unchanged: $5 + 4 + 2 = 11$ .

$5\sqrt{13} + 4\sqrt{13} + 2\sqrt{13} = 11\sqrt{13}$

This example extends the technique to more than two terms. Just as combining three like variable terms such as $5x + 4x + 2x = 11x$ works by adding all the coefficients at once, the same approach applies when the common factor is a square root rather than a variable.