## Key Questions

#### Explanation:

Example1: $\sqrt{5} + 2 \sqrt{5} = 3 \sqrt{5}$

Example 2: $6 \sqrt{2} - 2 \sqrt{2} = 4 \sqrt{2}$

If you can simplify the square root by using perfect squares to make them the same radical, do it using $\sqrt{m \cdot n} = \sqrt{m} \cdot \sqrt{n}$

Example 3: $6 \sqrt{8} - 2 \sqrt{2}$

Simplify $\sqrt{8} : \text{ } \sqrt{8} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2}$

$6 \sqrt{8} - 2 \sqrt{2} = 6 \cdot 2 \sqrt{2} - 2 \sqrt{2} = 12 \sqrt{2} - 2 \sqrt{2} = 10 \sqrt{2}$

• Like terms are terms whose variables are the same. If both terms do not have variables, then they are still like terms.

For example,

$4 x$ and $293 x$ are like terms.

$5 x y$ and $7 y$ are not like terms.

$\sqrt{5} x$ and $65 x$ are like terms.

$56 x {y}^{2}$ and $7 x y$ are not like terms.

$5$ and $9284$ are like terms.

As to your question, radicals on their own are like terms because they all do not have a variable.

$\sqrt{43}$ and $\sqrt{53}$ are like terms, as there are no variables on both of them.