Chapter A.10, Problem 30AYU

To determine

To find: Simplify the expression $2\sqrt{12}-3\sqrt{27}$.

Answer to Problem 30AYU

The value of $2\sqrt{12}-3\sqrt{27}=-5\sqrt{3}$.

Explanation of Solution

Given:

It is asked to find the simplest form of the given expression $2\sqrt{12}-3\sqrt{27}$.

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 $\sqrt{3}$ is the like radical in the given expression.

$2\sqrt{12}-3\sqrt{27}=2\sqrt{4\times 3}-3\sqrt{9\times 3}=2\sqrt{4}\times \sqrt{3}-3\sqrt{9}\times \sqrt{3}$

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

$\sqrt{3}\left(4-9\right)=-5\sqrt{3}$