1. Radicals Review

2. Pronounced: 2 times the square root of 7 OR 2 radical 7
Parts
Radical Sign
Radicand – the number underneath the radical sign
Coefficient
Radical
Pronounced: 2 times the square root of 7 OR radical 7

3. Simplest Radical Form
When you cannot factor any more perfect squares from the radicand
The radical cannot be simplified further
We always want our answers to be in simplest radical form

4. Getting Radicals into Simplest Radical Form
Steps
1. Look for the largest perfect square that’s a factor of the radicand.

5. Getting Radicals into Simplest Radical Form
Steps
2. Factor using the perfect square as one of the factors.

6. Getting Radicals into Simplest Radical Form
Steps
3. Take the square root of the factor that’s a perfect square. 4

7. Getting Radicals into Simplest Radical Form
Steps
4. Write the square root as the factor in front of the radical and leave the other factor under the radical.

8. Getting Radicals into Simplest Radical Form
Steps
5. If there’s a number in front of the radical, multiply the square root by it. 3

9. Tips for Getting Radicals into Simplest Radical Form
Always check if the radicand is perfect square!
Check if factorable by common perfect squares – 4, 9, 16, or 25
If the radicand is prime (or if its only factors are prime), then it’s in simplest radical form
Be persistent!
You don’t have to find the largest perfect square the first time you factor the radicand

10. Examples

11. Examples

12. Examples

13. Your Turn:
Write problems 1 – 6 in simplest radical form.

14. Your Turn:

15. What about…
18 𝑥 2

16. Or…
3 25 𝑥 6

17. Or Even…
5𝑥 32 𝑥 11

18. Your Turn:
3 48 𝑚 7
𝑥 3 𝑦 5

19. Multiplying Radicals Multiply like parts
coefficients * coefficients
radicand * radicand
Simplify the radical if necessary

20. Examples

21. Examples

22. Examples

23. Your Turn:

24. Seek and Solve!!!

25. What is rationalizing?
The process of algebraically removing a radical sign from one part of a fraction
We generally rationalize the denominator (But we can rationalize the numerator.)

26. Why rationalize? The result is easier to estimate and understand
Also shows up in solving limits (in calculus)

27. An expression with exactly one term
Monomial
An expression with exactly one term
Examples: 3x
–7x3
Non-Examples:
7x – 4
4y2 – 16y + 60

28. Rationalizing the Numerator
Exact same process as rationalizing the denominator, except that we focus on the numerator instead of the denominator.
Reappears in calculus