Chapter A.10, Problem 29AYU

To determine

To find: Simplify the expression $-\sqrt{18}+2\sqrt{8}$.

Answer to Problem 29AYU

The value of $-\sqrt{18}+2\sqrt{8}=-\sqrt{2}$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $-\sqrt{18}+2\sqrt{8}$.

Calculation:

Two or more radicals can be combined, provided that they have the same index and the same radicand. Such radicals are called like radicals.

Here $\sqrt{2}$ is the like radical in the given expression.

$-\sqrt{18}+2\sqrt{8}=-\sqrt{9\times 2}+2\sqrt{4\times 2}=-(\sqrt{9}\times \sqrt{2)}+2(\sqrt{4}\times \sqrt{2})$

$-(\sqrt{9}\times \sqrt{2)}+2\left(\sqrt{4}\times \sqrt{2}\right)=\sqrt{2}\left(-\sqrt{9}+2\sqrt{4}\right)=\sqrt{2}\left(-\sqrt{3^2}+2\sqrt{2^2}\right)$

$\sqrt{2}\left(-3+2\right)=-\sqrt{2}$