.

1. WHAT ARETHE PARTS OF A RADICAL
EXPRESSION/S(NOTATION)?
𝑛
𝑎
1. the symbol is the radical sign
2. a is the radicand
3. n is the index
The entire expression is called radical

2. -In mathematics, an equation is a
mathematical statement that
shows the equality of two
expression/s.
What is an equation?

3. 1. 𝑥 + 20 = 55
2. 5𝑥 − 7 = 13
3. 𝑥2
− 𝑥 − 2 = 0
4. 4𝑥3
+ 2𝑥2
-3x-4 = 0
Linear Equation
Linear Equation
Quadratic Equation
Cubic Equation

4. 1. 𝑥 + 20 = 55
2. 5𝑥 − 7 = 13
3. 𝑥2
− 𝑥 − 2 = 0
4. 4𝑥3
+ 2𝑥2
-3x-4 = 0
x = 35 APE
x = 4 APE
x=2, x=-1 Factoring,
Completing the Squares,
Using quadratic Formula
Synthetic Division

5. 𝒙 − 𝟑 − 𝟔 = 𝟎
Radical Equation

6. SOLVING
RADICAL
EQUATIONS

7. WHAT IS A RADICAL
EQUATION?
Equations containing radicals
with variables in the radicand
are called radical equations.

8. EXAMPLES OF RADICAL EQUATIONS
𝑥 − 3 − 6 = 0
2 + 𝐶 = 13
𝑥 − 1 = 9
3𝑥 = 3
𝑥 + 1 = 5
4
3𝑥 = 15

9. To solve radical equations
1. Place the radical expression on one side of the sign of
equality.
2. Raise both sides of the equation to the index power
to eliminate the radical.
3. solve and simplify.
HOW DO WE SOLVE RADICAL EQUATIONS?

10. Example 1 . Find the value of the of the
unknown quantity in the equation
𝒙 − 𝟑 − 𝟔 = 𝟎
1. Place the radical expression on one side of the sign
of equality.
𝒙 − 𝟑 = 𝟔
𝒙 − 𝟑 − 𝟔 = 𝟎

11. 2. Raise both sides of the equation to the
index power to eliminate the radical.
𝒙 − 𝟑 = 𝟔
𝒙 − 𝟑
𝟐
= 𝟔 𝟐
𝒙 − 𝟑 = 𝟑𝟔

12. 3. Solve and Simplify.
𝒙 − 𝟑 = 𝟑𝟔
𝒙 = 𝟑𝟔 + 𝟑
𝒙 = 𝟑𝟗

13. Check:
Substitute the value of the variable to the original equation.
𝒙 − 𝟑 − 𝟔 = 𝟎
𝟑𝟔 − 𝟔 = 𝟎
𝟑𝟗 − 𝟑 − 𝟔 = 𝟎
6−𝟔 = 𝟎 Correct

14. 3. 𝑥 − 3 − 6 = 0
2. 2 + 𝐶 = 13
4. 𝑥 − 1 = 9
6. 3𝑥 = 3
5. 𝑥 + 1 = 5
7.
4
3𝑥 = 15
8. 4 + 𝑥 − 2 = 𝑥

15. ACTIVITY
Solve the following radical equations
1. 𝑥 − 10 = 0
3.
4
2𝑚 = 4
5. 3
𝑥 = 12
4.
5𝑥
4
− 8 = 2
2. 2𝑥 + 5 = 7

16. ASSIGNMENT
 Solve the following problem sets. Show your solutions.
1.The square root of 1 more than twice a certain
number is 5. Find the number.
2.The square root of the product of 4 and a
number is 26. Find the number.
3.The square root of 5 more than twice a number
is 7. Find the number.