Question

simplify.

1. $7\sqrt{7} - 2\sqrt{7}$
2. $7\sqrt{5} + 4\sqrt{5}$
3. $12\sqrt{r} - 9\sqrt{r}$
4. $3\sqrt{5} - 2\sqrt{20}$
5. $5\sqrt3{17} + 2\sqrt3{17}$

Explanation:

Step1: Combine like radical terms

$7\sqrt{7} - 2\sqrt{7} = (7-2)\sqrt{7} = 5\sqrt{7}$

Step2: Combine like radical terms

$7\sqrt{5} + 4\sqrt{5} = (7+4)\sqrt{5} = 11\sqrt{5}$

Step3: Combine like radical terms

$12\sqrt{r} - 9\sqrt{r} = (12-9)\sqrt{r} = 3\sqrt{r}$

Step4: Simplify $\sqrt{20}$ first

$\sqrt{20} = \sqrt{4\times5} = 2\sqrt{5}$, so $2\sqrt{20}=2\times2\sqrt{5}=4\sqrt{5}$

Step5: Combine like radical terms

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

Step6: Combine like radical terms

$5\sqrt[3]{17} + 2\sqrt[3]{17} = (5+2)\sqrt[3]{17} = 7\sqrt[3]{17}$

Answer:

1. $5\sqrt{7}$
2. $11\sqrt{5}$
3. $3\sqrt{r}$
4. $-\sqrt{5}$
5. $7\sqrt[3]{17}$