HOW TO SOLVE RADICAL EQUATIONS

Solve the following radical equations.

Problem 1 :

3√x + 3 = 15

Solution :

Subtract 3 from both sides.

3√x = 12

Dividing by 3 on both sides

√x = 4

Take square on both sides.

x = 16

Problem 2 :

4√x - 1 = 3

Solution :

Add 1 from both sides.

4√x = 4

Divide by 4 on both sides.

√x = 1

Take square on both sides.

x = 1

Problem 3 :

√(x + 3) = 5

Solution :

Raise both sides to the power 2.

[√(x + 3)]² = (5)²

x + 3 = 25

x = 25 - 3

x = 22

Problem 4 :

√(3x + 4) = 4

Solution :

Raise both sides to the power 2.

[√(3x + 4)]² = (4)²

3x + 4 = 16

3x = 16 - 4

3x = 12

Divide by 3 on both sides.

x = 4

Problem 5 :

√(2x + 3) - 7 = 0

Solution :

Add 7 from both sides.

√(2x + 3) = 7

Raise both sides to the power 2.

[√(2x + 3)]² = 7²

2x + 3 = 49

2x = 46

x = 23

Problem 6 :

√(6 - 3x) - 2 = 0

Solution :

Add 2 from both sides.

√(6 - 3x) = 2

Raise both sides to the power 2.

[√(6 - 3x)]² = (2)²

6 - 3x = 4

-3x = 4 - 6

-3x = -2

x = 2/3

Problem 7 :

x^1/4 - 1 = 0

Solution :

x^1/4 - 1 = 0

Add 1 from both sides.

x^1/4 = 1

Raise both sides to the power 4.

(x^1/4)⁴ = (1)⁴

x = 1

Problem 8 :

(x - 2)^1/3 = -5

Solution :

Raise both sides to the power 3.

[(x - 2)^1/3]³ = (-5)³

x - 2 = -125

x = -125 + 2

x = -123

Problem 9 :

x^1/3 - 2 = 0

Solution :

Add 2 on both sides.

x^1/3  = 2

Raise both sides to the power 3.

(x^1/3)³ = (2)³

x = 8

Problem 10 :

√3x = 6

Solution :

Raise both sides to the power 2.

(√3x)² = (6)²

3x = 36

x = 12 

Problem 11 :

(2x + 7)^1/2 - x = 2

Solution :

Add x from both sides.

(2x + 7)^1/2 = 2 + x

Raise both sides to the power 2.

[(2x + 7)^1/2]² = (2 + x)²

Using the identity (a + b)² = a² + 2ab + b² on the left side,

2x + 7 = 4 + 4x + x²

x² + 4x - 2x - 7 + 4  = 0

x² + 2x - 3 = 0

(x - 1) (x + 3) = 0

x = 1, -3

Problem 12 :

√4x - 8 = 0

Solution :

Add 8 from both sides.

√4x = 8

Raise both sides to the power 2.

(√4x)² = (8)²

4x = 64

x = 16