Multiplying Radical Expressions 03:20 minutes

Video Transcript

Transcript Multiplying Radical Expressions

We join our hero, Snipe, after scaling the Mushroom Mountain, running through the Mushroom Forest and searching for the Mushroom Castle. His journey is almost complete. He needs one more piece to complete the door of wisdom. Snipe has traversed Mushroom Mountain and has finally collected all the lost pieces he needs to enter the Mushroom Castle. He only gets one shot at correctly completing the door of wisdom. Otherwise, something bad will happen. To do this, he must know how to multiply radical expressions.

Multiplying radical expressions

Snipe opens his bag to reveal the stones he’s collected on his journey. If he’s able to open the door of wisdom, he can prove he’s worthy of the riches inside. Each of the stones he collected has markings that look like mathematical equations. If he’s able to solve these equations, maybe they’ll tell him which one belongs in the door of wisdom. Snipe looks at the door and then down at his keys. Surely one of these will open the Door of Wisdom. Snipe examines the first key.

Since both the expressions are in parentheses, Snipe decides to FOIL them. First, Outer, Inner, Last. Snipe multiplies the factors outside the radicals first. He then uses the Multiplication Property of Radicals to simplify the factors under the radical. He does this for all terms, then he combining the like terms, removing any squares from under the radicals and finally, once again combining like terms gives us ew. This is kind of a messy answer. Maybe our hero'll have better luck with the other keys.

First we FOIL until we can't FOIL no mo', then combine like terms. But there are none, so we move on to the next step and remove any squares from under the radicals. Here, you don't see any squares at first glance, but 18 can be factored into 2 and 9, which is a perfect square.

Using the Multiplication Property of Radicals in reverse, we split the radical in two and take the square root of 9. A bit of PEMDAS and that’s the simplified version? This is definetely not the right key. Last key, and the last hope for our hero. FOIL, just like the others: 1. Combine like terms once again 2. Remove any squares from under the radicals

This is looking quite promising! And Done! Woohoo! Behold! The key that unlocks the Door of Wisdom! Snipe identifies the shape needed to open the door and carefully slides it into place.