Question

Simplify

1. $5\sqrt{3}-9\sqrt{3}$
   
2. $5\sqrt[3]{y}+3\sqrt[3]{y}$
   
3. $5\sqrt[4]{m}-2\sqrt[3]{m}$
   

Short answer

Part a. $-4\sqrt{3}$

Part b. $8\sqrt[3]{y}$

Part c.$5\sqrt[4]{m}-2\sqrt[3]{m}$

Step-by-step solution

Part (a) Step 1. Subtract the like radicals to simplify 

In the expression $5\sqrt{3}-9\sqrt{3}$, the radicals are like. So we subtract the coefficients to get the simplified expression.

$\begin{array}{rcl}5\sqrt{3}-9\sqrt{3}& =& (5-9)\sqrt{3}\\ & =& -4\sqrt{3}\end{array}$

Part (b) Step 1. Add the like radicals to simplify  

In the expression $5\sqrt[3]{y}+3\sqrt[3]{y}$, the radicals are like. So we add the coefficients to get the simplified expression.

$\begin{array}{rcl}5\sqrt[3]{y}+3\sqrt[3]{y}& =& (5+3)\sqrt[3]{y}\\ & =& 8\sqrt[3]{y}\end{array}$

Part (c) Step 1. Check the indices and the radicals 

In the given expression $5\sqrt[4]{m}-2\sqrt[3]{m}$the radicals are the same but the indices are different. So they are not like radicals.

Since the radicals are not like so we cannot subtract them.