Problem 37 - College Algebra

Question

Add or subtract terms whenever possible. $$\sqrt{8}+3 \sqrt{2}$$

Step-by-Step Solution

Answer

The simplified form of \(\sqrt{8} + 3\sqrt{2}\) is \(5\sqrt{2}\)

Step 1: Simplify the square root of 8

First, factor the number under the square root into a product of a perfect square and another number. That is, \(\sqrt{8}\) equals \(\sqrt{4*2}\) which simplifies to \(2\sqrt{2}\).

Step 2: Combine like terms

Now, with \(\sqrt{8}\) simplified to \(2\sqrt{2}\), we add this to our other term. Combine \(2\sqrt{2}\) with \(3\sqrt{2}\) to get \(5\sqrt{2}\).