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Add. Write your answer in simplest form. $\newline$ $-\sqrt{5} + 9\sqrt{5}$

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Add and subtract radical expressions

Full solution

Q. Add. Write your answer in simplest form.

\newline

-\sqrt{5} + 9\sqrt{5}

Combine Like Terms: Combine the like terms $-\sqrt{5}$ and $9\sqrt{5}$ . $\newline$ Since both terms have the same radical part, $\sqrt{5}$ , we can add the coefficients directly. $\newline$ $-\sqrt{5} + 9\sqrt{5} = (-1 + 9) \times \sqrt{5}$
Add Coefficients: Perform the addition of the coefficients. $\newline$ $-1 + 9 = 8$
Multiply Result: Multiply the result from Step $2$ by the common radical part. $\newline$ $8 \times \sqrt{5} = 8\sqrt{5}$ $\newline$ This is the simplest form since $8$ and $5$ have no common factors, and $5$ is not a perfect square.

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