SOLVING RADICAL EQUATIONS WORKSHEET

Find the extraneous solution for the radical equations given below.

Problem 1 :

√(x + 4) = x - 2      Solution

Problem 2 :

√(10x + 9) = x + 3     Solution

Problem 3 :

√(2x + 5) = √(x + 7)     Solution

Problem 4 :

4)  √(x + 6) – 2 = √(x – 2)     Solution

Problem 5 :

In a hurricane, the mean sustained wind velocity v (in meters per second) can be modeled by v( p) = 6.3 √(1013 − p), where p is the air pressure (in millibars) at the center of the hurricane. Estimate the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second.

Solution

Problem 6 :

Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 62.5 ³√t + 75.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 250 centimeters

Solution

Solve the following radical equations with rational exponents.

Problem 1 :

2x^(2/3) = 8

Solution

Problem 2 :

4x^(3/2) = 32

Solution

Problem 3 :

 x^1/4 + 3 = 0

Solution

Problem 4 :

2x^3/4 - 14 = 40

Solution

Problem 5 :

(x + 6)^1/2 = x

Solution

Problem 6 :

(5 - x)^1/2 – 2x = 0

Solution

Problem 7 :

2(x + 11)^1/2 = x + 3

Solution

Problem 8 :

(5x² – 4)^1/4 = x

Solution

Problem 9 :

x^1/5 = 2

Solution

Problem 10 :

2√(3x – 1) + 3 = 11

Solution

Problem 11 :

4x² = 64

Solution

Problem 12 :

2(x – 2)⁴ – 3 = 159

Solution

Problem 13 :

√(2x + 4) = √(x + 2)

Solution

Problem 14 :

 ∛x – 6 = -2

Solution

Problem 15 :

3 = (2x + 7)^1/4

Solution

Problem 16 :

Let f(x) = 6x and g(x) = x^3/4. Find ( f/g ) (x), then evaluate the quotient when x = 16.

Solution

Solve the following radical equations :

Problem 1 :

√(x + 1) = 4

Solution

Problem 2 :

√(2t + 15) = t

Solution

Problem 3 :

√(p - 4) = -5

Solution

Problem 4 :

√(2 – x) = x - 2

Solution

Problem 5 :

√s² – 1 = √5s – 5

Solution

Problem 6 :

∛x = 4

Solution

Problem 7 :

∜(2p + 2) = 3

Solution

Problem 8 :

∛x + 1 = ∛x² - 5

Solution

Problem 9 :

√(2 - √x) = √x

Solution

Problem 10 :

√(3a + 16) - 3 = a - 1

In the equation above, a ≥ 0, which of the following is a possible value of a ?

a)  3      b)  2      c)  1     d)  0

Solution

Problem 11 :

8 + [√(2x + 29)/3] = 9

For what value of x is this equation true ?

a)  -10      b)  -12      c)  19     d)  No solution

Solution

Problem 12 :

3x = x + 14

√(3z² - 11) + 2x = 22

If z > 0, what is the value of z ?

Solution

Solve the following radical equations.

Problem 1 :

3√x + 3 = 15

Solution

Problem 2 :

4√x - 1 = 3

Solution

Problem 3 :

√(x + 3) = 5

Solution

Problem 4 :

√(3x + 4) = 4

Solution

Problem 5 :

√(2x + 3) - 7 = 0

Solution

Problem 6 :

√(6 - 3x) - 2 = 0

Solution

Problem 7 :

x^1/4 - 1 = 0

Solution

Problem 8 :

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

Solution

Problem 9 :

x^1/3 - 2 = 0

Solution

Problem 10 :

√3x = 6

Solution

Problem 11 :

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

Solution

Problem 12 :

√4x - 8 = 0

Solution

Problem 13 :

In an amusement park ride, a rider suspended by cables swings back and forth from a tower. The maximum speed v (in meters per second) of the rider can be approximated by v = √2gh, where h is the height (in meters) at the top of each swing and g is the acceleration due to gravity (g ≈ 9.8 m/sec²). Determine the height at the top of the swing of a rider whose maximum speed is 15 meters per second.

Solution

Problem 14 :

(5x² − 4)^1/4 = x

Solution

Problem 15 :

2(x + 11)^1/2 = x + 3

Solution

SAT Practice Questions On Radicals

• Practice questions on SAT
• Practice questions on squares and square roots
• Solving radical equations with square roots