**Video Transcript**

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Transcript
**Solving Radical Equations**

Leo Vitruvian, the polymath, is good at many things. He's an inventor, a painter and quite the mathematician. A local banker, Lorenzo Medici, has asked Leo to create the world's first flying machine. Lorenzo would like Leo to paint the propellers in the colors of his family's crest, so he gives Leo some special instructions, which he delivers on a scroll, of course. To complete the task correctly, Leo must be able to **solve radical equations**.

Leo Vitruvian goes down to his local paint shop in search of the special palette of paints. There are so many colors! It’s like a color library! Let’s take a closer look at Leo Vitruvian’s instructions. No! The paint shop has a different labeling system! The shop owner looks utterly confused.

### Isolating the radical

Starting with the first equation, we have the **square root** of 'x', plus 6, equals 9. When **solving radical equations**, it's good to first try and **isolate the radical**. Here, we use **opposite operations** to **isolate** the **square root** of 'x'. Next, we **square** both sides, giving us our answer, 9. Leo Vitruvian can safely purchase this color.

The other equations don’t look so simple. The next color on the list is 4 equals 2 root quantity 'x' over 3. Even though this equation looks different, let's see if following our checklist still works. First, we **isolate** the **radical** by **dividing** both sides by 2. Next, we **square both sides** - just like before. And finally, we **isolate** the 'x' using **opposite operations**. Leo Vitruvian adds this color to his basket as well.

### Equations with two Radicals

The next equation is uh oh Leo's in trouble...two radicals?! One on each side?! It's going to be hard to **isolate** these radicals, so let's just **square** both sides and get rid of them. That's looking a whole lot better! Now just solve by using **PEMDAS**!

These equations just keep looking messier and messier. But Leo sticks with his checklist. ‘x' equals the square root of the quantity 2x plus 8. The radical is already isolated, so he must have to square both sides to get rid of the radical. This equation looks familiar. Leo must've used it in another painting he did for Lorenzo. Leo Vitruvian recognizes that he can put this **quadratic equation** into **standard form**. Then he'll have several ways to solve it! Leo goes for **factoring**, since the numbers are playing nice. He finds the **solution** and adds this color to his basket.

With all the colors selected and purchased, Leo Vitruvian goes to paint the flying machine. He’s just putting on the final touches. Time to test!