Problem 38 - College Algebra

Question

Add or subtract terms whenever possible. $$\sqrt{20}+6 \sqrt{5}$$

Step-by-Step Solution

Answer

The simplified form of the given expression is \( 8 \sqrt{5} \)

Step 1: Simplify the Radicals

First, each term needs to be simplified to its simplest radical form. The square root of 20 can be simplified by breaking 20 into its prime factors, which are 2 and 5. So, \( \sqrt{20} \) can be written as \( 2 \sqrt{5} \). The equation now becomes \( 2 \sqrt{5} + 6 \sqrt{5} \).

Step 2: Add Like Terms

Since both terms are similar (\( \sqrt{5} \)), we can add the numbers in front of them. This is similar to adding variables. Here, we will add 2 and 6. So, \( 2 \sqrt{5} + 6 \sqrt{5} \) becomes \( 8 \sqrt{5} \)