# Adding and Subtracting Radical Expressions 03:34 minutes

**Video Transcript**

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Transcript
**Adding and Subtracting Radical Expressions**

Meet Clara and her roommate, Maxine. Clara is a very free spirit. This is fine most of the time, but to the chagrin of Maxine, Clara likes to combine everything and Clara cooks for the both of them. Banana and Steak Tacos, Cake and Nacho Cheese, Fish and Chocolate. One day, while sleeping, Maxine slipped some new listening material into Clara’s playlist with one message: stop combining things that shouldn’t be combined. Max doesn’t know how many more blueberry marshmallow pizzas she can eat. The next day, expecting another honey cauliflower salmon dish, Clara’s roommate is pleasantly surprised to be presented with a tasty looking spread. Maxine is ecstatic and curious about what was on the tape.

## Adding and Subtracting Radical Expressions

What a weird title for a self-improvement tape. **Adding** and **Subtracting Radical Expressions**. Let’s take a listen: Welcome to the relaxation zone, you are fully relaxed. Your eyes are getting heavy. You should combine things like you Add and Subtract Radical Expressions.
Radical expressions look daunting, but they’re not. Radical expressions are your friends. Radical expressions are not hard.

Let’s take a closer look. If we have 4 times the **square root** of 3 plus 5 root 5 plus 6 root 3 minus 2 root 5, we have to first take a look at how many different numbers we have under the **radical**. In this **equation**, the **numbers** under the **radical** are 3 and 5.
First, we have to replace the square root of 3 with ‘x’ and root 5 with ‘y’.
Now, we can **add** the **terms** together using the rules we already know for **adding variables**. 4x + 6x = 10x and 5y - 2y = 3y. After we’re sure we’ve simplified things as much as possible, now we can simply plug our roots back in and finish solving the problem.

After **substituting** the square roots back into the original equation, we get 10 times the square root of 3 plus 3 times the square root of 5. Now, we just have to plug this into our calculator to find the answer: this is about 24.03.

### Instruction to add and subtract Radical Expressions

Let’s review the steps again, this time, using different numbers.
Step 1: Identify how many different **roots** there are in the **expression** and assign each one a letter.
Step 2: Replace all instances of the root with the same **variable**.
Step 3: **Solve** the equation with the same rules for adding variables.
Step 4: Re-replace the variables with the original **square roots**.
Step 5: As always, **PEMDAS**.

Now that we know how to add and subtract radical expressions, let’s get back to the roommates and see what’s cooking. Would ya look at that? Maxine cooked! Clara looks impressed for now.

**All Video Lessons & Practice Problems in Topic**Radical Expressions / Equations »