Q 8.71. - Intermediate Algebra

Question

Simplify: 

1. $8\sqrt{2}-9\sqrt{2}$
   
2. $4\sqrt[3]{x}+7\sqrt[3]{x}$
   
3. $3\sqrt[4]{x}-5\sqrt[4]{y}$
   

Step-by-Step Solution

Answer

Part a. $-\sqrt{2}$

Part b. $11\sqrt[3]{x}$

Part c.  $3\sqrt[4]{x}-5\sqrt[4]{y}$

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

In the expression $8\sqrt{2}-9\sqrt{2}$, the radicals are like. So we subtract the coefficients to get the simplified expression.

$\begin{array}{rcl}8\sqrt{2}-9\sqrt{2}& =& (8-9)\sqrt{2}\\ & =& -\sqrt{2}\end{array}$

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

In the expression $4\sqrt[3]{x}+7\sqrt[3]{x}$, the radicals are like. So we add the coefficients to get the simplified expression.

$\begin{array}{rcl}4\sqrt[3]{x}+7\sqrt[3]{x}& =& (4+7)\sqrt[3]{x}\\ & =& 11\sqrt[3]{x}\end{array}$

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

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

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