Chapter A.10, Problem 27AYU

To determine

To find: Simplify the expression $3\sqrt{2}+4\sqrt{2}$.

Answer to Problem 27AYU

The value of $3\sqrt{2}+4\sqrt{2}=7\sqrt{2}$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $3\sqrt{2}+4\sqrt{2}$.

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.

$3\sqrt{2}+4\sqrt{2}=\left(3+4\right)\sqrt{2}=7\sqrt{2}$