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Add. Write your answer in simplest form. $\newline$ $2\sqrt{2} + 9\sqrt{2}$

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Add and subtract radical expressions

Full solution

Q. Add. Write your answer in simplest form.

\newline

2\sqrt{2} + 9\sqrt{2}

Combine like terms: Combine the like terms $2\sqrt{2}$ and $9\sqrt{2}$ . Since both terms have the same radical part, $\sqrt{2}$ , we can add the coefficients directly. $2\sqrt{2} + 9\sqrt{2} = (2 + 9)\sqrt{2}$
Simplify expression: Simplify the expression by adding the coefficients. $\newline$ $(2 + 9)\sqrt{2} = 11\sqrt{2}$ $\newline$ This is the simplest form since $11$ and $2$ have no common factors other than $1$ , and the square root of $2$ cannot be simplified further.

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