Q. 8.74 - Intermediate Algebra

Question

Simplify

1. $4\sqrt{3y}-7\sqrt{3y}+2\sqrt{3y}$
   
2. $6\sqrt[3]{7mn}+\sqrt[3]{7mn}-4\sqrt[3]{7mn}$
   

Step-by-Step Solution

Answer

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

Part b. $3\sqrt[3]{7mn}$

Part (a) Step 1. Combine the like radicals

In the expression $4\sqrt{3y}-7\sqrt{3y}+2\sqrt{3y}$ , all the radicals are like and so we can combine them. On combining them we get

$\begin{array}{rcl}4\sqrt{3y}-7\sqrt{3y}+2\sqrt{3y}& =& (4-7+2)\sqrt{3y}\\ & =& -\sqrt{3y}\end{array}$

Part (b) Step 1. Combine the like radicals

In the expression $6\sqrt[3]{7mn}+\sqrt[3]{7mn}-4\sqrt[3]{7mn}$, all the radicals are like and so we can combine them. On combining them we get

$\begin{array}{rcl}6\sqrt[3]{7mn}+\sqrt[3]{7mn}-4\sqrt[3]{7mn}& =& (6+1-4)\sqrt[3]{7mn}\\ & =& 3\sqrt[3]{7mn}\end{array}$