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Add. Write your answer in simplest form. $\newline$ $-4\sqrt{2} + 5\sqrt{2}$

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Add and subtract radical expressions

Full solution

Q. Add. Write your answer in simplest form.

\newline

-4\sqrt{2} + 5\sqrt{2}

Combine like terms: Combine the like terms $-4\sqrt{2}$ and $5\sqrt{2}$ . $\newline$ Since both terms have the same radical part, $\sqrt{2}$ , we can add the coefficients directly. $\newline$ $-4\sqrt{2} + 5\sqrt{2} = (-4 + 5)\sqrt{2}$
Perform coefficient addition: Perform the addition of the coefficients. $\newline$ $-4 + 5 = 1$ $\newline$ So, the expression becomes $1\sqrt{2}$ .
Simplify expression: Simplify the expression. $1\sqrt{2}$ is simply written as $\sqrt{2}$ , since $1$ times any number is the number itself.

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