Q 8.73. - Intermediate Algebra

Question

Simplify

1. $\sqrt{7x}-7\sqrt{7x}+4\sqrt{7x}$
   
2. $4\sqrt[4]{5xy}+2\sqrt[4]{5xy}-7\sqrt[4]{5xy}$
   

Step-by-Step Solution

Answer

Part a. $-2\sqrt{7x}$

Part b. $-\sqrt[4]{5xy}$

Part (a) Step 1. Combine the like radicals

In the expression $\sqrt{7x}-7\sqrt{7x}+4\sqrt{7x}$ all the radicals are like and so we can combine them. On combining them we get

$\begin{array}{rcl}\sqrt{7x}-7\sqrt{7x}+4\sqrt{7x}& =& (1-7+4)\sqrt{7x}\\ & =& -2\sqrt{7x}\end{array}$

Part (b) Step 1. Combine the like radicals

In the expression $4\sqrt[4]{5xy}+2\sqrt[4]{5xy}-7\sqrt[4]{5xy}$, all the radicals are like so we can combine them. On combining them we get

$\begin{array}{rcl}4\sqrt[4]{5xy}+2\sqrt[4]{5xy}-7\sqrt[4]{5xy}& =& (4+2-7)\sqrt[4]{5xy}\\ & =& -\sqrt[4]{5xy}\end{array}$