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Preparatory Activity
Solve the given equation.
1. 4𝑚 − 2 = 6
2.
𝑋
2
− 3 = 1
3.
3
2
+ 𝑥 = 2
4.
4
5
𝑥 =
27
5
5. 3𝑥 + 5 = 35
6. 2 𝑥 − 7 = 3 𝑥 + 1
EQUATIONS
WITH RADICALS
A radical equation is an equation whose
radicand contains an unknown variable.
 The following are examples of radical equations:
𝑥 − 1 = 5
2 𝑥 + 1 = 2
3
𝑥 = 1 + 𝑥
Guidelines in Solving
Radical Equations
Place or isolate one of the radical terms.
Apply the principle of powers.
If the radical remains, perform steps 1 and 2
again.
Check for possible solutions.
LETS TRY TO SOLVE THE FOLLOWING:
1. 𝑥 − 1 = 2
2. 3𝑥 + 2 = 3
3. 𝑥 + 1 = 3
4.
3
𝑥 + 5 = 2
5. 𝑥 + 5 − 2 𝑥 = 0
More Examples:
1. 3𝑥 + 4 = 8
2. 2𝑧 + 3 + 5 = 0
3.
3
𝑎 − 1 = 4
4. 𝑚2 − 4𝑚 + 9 = 𝑚 − 1
ITS YOUR TURN!
Warm-Up Practice
Page 32
ACTIVITY A
ODD items ONLY

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1 lesson 5 equations with radicals

  • 2. Solve the given equation. 1. 4𝑚 − 2 = 6 2. 𝑋 2 − 3 = 1 3. 3 2 + 𝑥 = 2 4. 4 5 𝑥 = 27 5 5. 3𝑥 + 5 = 35 6. 2 𝑥 − 7 = 3 𝑥 + 1
  • 4. A radical equation is an equation whose radicand contains an unknown variable.  The following are examples of radical equations: 𝑥 − 1 = 5 2 𝑥 + 1 = 2 3 𝑥 = 1 + 𝑥
  • 5. Guidelines in Solving Radical Equations Place or isolate one of the radical terms. Apply the principle of powers. If the radical remains, perform steps 1 and 2 again. Check for possible solutions.
  • 6. LETS TRY TO SOLVE THE FOLLOWING: 1. 𝑥 − 1 = 2 2. 3𝑥 + 2 = 3 3. 𝑥 + 1 = 3 4. 3 𝑥 + 5 = 2 5. 𝑥 + 5 − 2 𝑥 = 0
  • 7. More Examples: 1. 3𝑥 + 4 = 8 2. 2𝑧 + 3 + 5 = 0 3. 3 𝑎 − 1 = 4 4. 𝑚2 − 4𝑚 + 9 = 𝑚 − 1
  • 8. ITS YOUR TURN! Warm-Up Practice Page 32 ACTIVITY A ODD items ONLY