SOLVING RADICAL EQUATIONS WITH EXTRANEOUS SOLUTIONS WORKSHEET

Find the extraneous solution for the radical equations given below.

Problem 1 :

√(x + 4) = x - 2

Problem 2 :

√(10x + 9) = x + 3

Problem 3 :

√(2x + 5) = √(x + 7)

Problem 4 :

√(x + 6) – 2 = √(x – 2)

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.

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

Problem 1 :

Solve x + 1 = √(7x + 15)

Solution

Problem 2 :

Solve √(x + 2) + 1= √(3 – x)

Solution

Problem 3 :

√(10 - x) = x + 2

Solution

Problem 4 :

(2x)^3/4 + 2 = 10

Solution

Problem 5 :

(x + 30)^1/2 = x

Solution

Problem 6 :

√(5x + 1) = 6

Solution

Problem 7 :

√(x + 2) + 1 = √(3 - x)

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

Solve the following radical equation

Problem 1 :

√(4x + 1) = √(x + 10)

Solution

Problem 2 :

√(3x – 3) - √(x + 12) = 0

Solution

Problem 3 :

∛2x – 5 - ∛8x + 1 = 0

Solution

Problem 4 :

∛(x + 5) = 2∛(2x + 6)

Solution

Problem 5 :

√(3x – 8) + 1 = √(x + 5)

Solution

Problem 6 :

√(x + 2) = 2 - √x

Solution

Problem 7 :

√(2x + 4) = √(x + 2)

Solution

Problem 8 :

The lateral surface area of a right circular cone, s, is represented by the equation 

s = πr√(r² + h²)

where r is the radius of the circular base and h is the height of the cone. If the lateral surface area of a large funnel is 236.64 square centimeters and its radius is 4.75 centimeters, find its height, to the nearest hundredth of a centimeter.

Solution

Problem 9 :

Solve algebraically for x: 

√(x² + x - 1) + 11x = 7x + 3

Solution