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Add. Write your answer in simplest form. $\newline$ $-2\sqrt{2} + 7\sqrt{2}$

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Add and subtract radical expressions

Full solution

Q. Add. Write your answer in simplest form.

\newline

-2\sqrt{2} + 7\sqrt{2}

Combine like terms: Combine the like terms $-2\sqrt{2}$ and $7\sqrt{2}$ . Since both terms have the same radical part, $\sqrt{2}$ , we can add the coefficients directly. $-2\sqrt{2} + 7\sqrt{2} = (-2 + 7)\sqrt{2}$
Perform coefficient addition: Perform the addition of the coefficients. $\newline$ $-2 + 7 = 5$ $\newline$ So, the expression becomes $5\sqrt{2}$ .
Check for simplification: Check for any possible simplification. $\newline$ The term $5\sqrt{2}$ is already in its simplest form since $5$ is a prime number and cannot be factored out with the radical.

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