Problem 81 - College Algebra

Question

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

Step-by-Step Solution

Answer

\(\sqrt{2} + \sqrt[3]{8} = \sqrt{2} + 2\)

Step 1: Identify the Radicands

First, identify the radicand of both terms. The radicand is the number or expression underneath the radical. In this case, the radicands are \(2\) and \(8\).

Step 2: Simplify Square Root

The square root of 2 is already in its simplest form. This is because 2 is a prime number, and cannot be factored further.

Step 3: Simplify Cube Root

The cube root of 8 can be simplified, because 8 can be written as 2 * 2 * 2. The cube root of 8 is therefore 2.

Step 4: Add the Simplified Terms

Now add together the square root of 2 and the cube root of 8 which was simplified as 2. Therefore, \(\sqrt{2} + \sqrt[3]{8} = \sqrt{2} + 2\)