1. Square Roots Simplifying Square Roots
Multiplying and Dividing Square Roots
Adding and Subtracting Square Roots
Using square roots with the distance formula
Solving Radical Equations

2. Simplifying Square Roots
When you find the square root of a number on your calculator, you usually must round the answer.
To get the exact answer you must simplify the square root.
Some square roots will be a whole number answer.
To be a whole number answer, the number you are taking the square root of will be a perfect square.
What are some perfect squares??

3. Square rooting perfect squares
225 =
100 =
36 =
625 =
81 =

4. Simplifying Square Roots
How do you find the square root of a number that is not a perfect square?
What prime factors go into 112?
Start with 2 if the number is even.
Divide by prime factors until you get a 1 on the left side of your line.
This is a factor tree “stump”
112 2 56 2 28 2
Circle the pairs of numbers on the right.
Multiply the numbers in each pair together and put in front of the radical.
Any left over numbers should be multiplied together and left under the radical. 14 2 7 7 1
2•2 7 = 4 7

5. Try a few.

6. Try some with variables.
216 𝑛 𝑎 3 𝑏 𝑐 7

7. Simplify the following square roots, leave all answers in radical form.

8. Simplifying square roots with variables.
98 𝑥 𝑛 𝑥 6
7 84 𝑚 𝑥 𝑡 3

9. Multiplying Square roots
How do you multiply square roots?
Multiply the numbers under the radical
Simplify the square root
7 • 7 49 7
5 • 15 75
5 3

10. Multiply Square roots with numbers in front of the square root
Multiply the numbers under the radical
Multiply the numbers in front of the radical
Simplify the square root
3 7 • 5 21
3•5 7•21
105 3
• 3 15
2•3 10 •15
6 150
30 6

11. Dividing Square Roots
When dividing square roots, you must get rid of the radical in the denominator
This is called rationalizing the denominator
Multiply the numerator and denominator by the radical in the denominator
Simplify the fraction and square roots within the fraction

12. 3 20 2 5 • 5 5 35 5 • 5 5 3 5 • 5 5 Divide square roots 30 10 = 3• •5
3•10 10
= 3 •
175 5 7 •

13. Adding Square And subtracting Square Roots
When adding and subtracting square roots, the radicals must be the same.
Make sure the radicals have the same number.
Add or subtract the number in front of the radical, but leave the radical and what’s in it alone.
If the numbers inside the radical are not the same then you can not put them together.
Adding and subtracting square roots is like adding and subtracting like terms.

14. Adding and Subtracting Square Roots

15. Try some problems

16. Applying Square Roots using the distance Formula
(3, -2), (5, 3)
d = (3 −5) 2 + (−2 −3) 2
d = (−2) 2 + (−5) 2
d =
d = 29
(9, 4), (4, -2)
d = (9 −4) 2 + (4 −(−2)) 2
d = (5) 2 + (6) 2
d =
d = 61

17. What is the distance between these points??
(4, 7), (9, 3)
(-2, -4), (-6, 3)
(10, -3), (15, 2)
(5, 4), (5, -3)

18. Solving Radical Equations
When solving radical equations you want to try to get rid of the square roots.
You can square both sides of the equation to get rid of the square root.
After the square root is gone, then solve the equation for the given variable.

19. Solve the following Radical equations
𝑥 = 𝑥 −5 = = 2𝑥+8
2 𝑥 −5 = 𝑥 = 𝑥 5 = 2𝑥 −9