2. At the end of the lesson, you are expected to:
•solve equations containing radicals;
•recognize extraneous solutions; and
•solve application problems that involve
radical equations as part of the solution.
3. Solve the riddle by matching the letters of the
following equations ton its solution/s below
3x + 5 = 8 R 10(x – 1) = 20 E
3x = x – 20 B x2 – 7x – 8 = 0 T
17 – 4x = 6x – 3 L x2 = 25 S
“IT IS THE END OF TIME AND PLACE AND THE
BEGINNING OF EVERY END”
E T E
2 -1,8 1 3
1
-10
2
3
-1,8
5
L T R E
4. What is a radical equation?
• A radical equation is an equation where the unknow
quantity appears under the radical sign.
• In solving radical equations, we assume that if two
numbers are equal, then their squares, cubes or nth
powers are also equal.
In symbols
If x = y, then xn = yn for every positive integer n.
5. Tell whether the given equation is a
radical equation or not. Show your
happy face if it represents a radical
equations otherwise; a sad face if it is
not.
12. Solution or Root
- a number that satisfy
the equation.
Not Solution or
Extraneous Root
- a number that does
not satisfy the
equation.
13. Determine whether the given value
of x is a solution of the equation.
Show LIKE SIGN if the given value
satisfied given equation and UNLIKE
SIGN if it is not.
19. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots.
21. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots. Extraneous roots are numbers
obtained when solving an equation that is not a solution of
the original equation.
23. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots. Extraneous roots are numbers
obtained when solving an equation that is not a solution of
the original equation.
25. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots. Extraneous roots are numbers
obtained when solving an equation that is not a solution of
the original equation.
27. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots. Extraneous roots are numbers
obtained when solving an equation that is not a solution of
the original equation.
29. To solve radical equations:
1. Isolate the radical on the left side by applying appropriate
properties of equality.
2. Combine similar terms whenever possible.
3. Get the nth root of both sides of the equation. This will
remove the radical sign.
4. Solve the resulting equation.
5. Check the solutions in the given equation for a possible
presence of extraneous roots. Extraneous roots are numbers
obtained when solving an equation that is not a solution of
the original equation.
30. Example 6
The time t (in seconds) that it takes an
object to have a free fall at a distance of d
feet from rest is given by the formula 𝑡 =
2𝑑
𝑔
,
where g is the acceleration due to gravity.
Solve for d.
31. Match each radical equation with its
correct solution. Be sure to check for
extraneous solutions. When finished,
fill in the missing letters to decode
the hidden message.
32. 1. 𝑥+ 3 = 7
2. 𝑥 + 10 = 2
3. 9 = 𝑥 + 7
4. 3 𝑥 + 𝑥2
= 15 + 𝑥2
5. 𝑥 + 5+ 1 = 3
6. 2 𝑥 + 7 =5
7. 5𝑥 − 2 = 𝑥 + 6
8. 𝑥 = 6𝑥 − 15
9. 5𝑥 − 9− 𝑥 = −1
10. x − 3 = 30 − 2𝑥
11. 𝑥2 − 𝑥 − 2 = 4
12. 𝑥 + 5 = 𝑥2 + 5
13. 𝑥2 + 4𝑥 + 4 = 3𝑥
A. x = 0, 1
B. x = 16
C. x = 2
D. x = 3
E. x = 2, 5
F. x = 7
G. x =-3, 7
I. x =-2, 3
L. x = -1
R. x = -6
S. x = 4
T. x = 25
V. X = -½, 1
Y. x = 1
__ __ __ __ __ __ __
12 5 10 9 1 2 12
__ __ __ __ __ __ __ __
12 7 4 11 13 11 4 6
__ __ __
11 3 12
__ __ __ __ __ __ __
2 12 8 11 7 12 5
DECODE THE MESSAGE
B R
R
S
T T
L
L
Y
C
C
D
E
G
I
I
I I
A A
A
A A
A V
33. Choose the word FACT if the
term being identified is correct. If the
term being identified is BLUFF,
identify the correct term.
34. or
Extraneous roots are numbers
obtained when solving an equation
that is not a solution of the original
equation.
35. or
A radical equation is an equation
where the unknown quantity appears
under the radical sign.
36. or
To eliminate the square root, we need
to cube both sides of the equations.
37. or
In solving radical equations, we assume
that if two numbers are equal, then
their squares, cubes of nth power are
also equal.
