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« Solving Quadratic Equation
Solving Equations: (lesson 4 of 4)

Solving Equations with Radicals

A "radical" equation is an equation in which there is a variable inside the radical sign

Four steps to solve equations with radicals

Step 1: Isolate the radicals to left side of the equal sign.

Step 2: Square each side of the equation

Step 3: Solve the resulting equation

Step 4: Check all solutions

Equations with one radical

Example 1: Solve Equation with one radical

Solution

Step 1: Isolate the radicals to left side of the equal sign.

Equation with one radical Step 1

Step 2: Square each side of the equation

Equation with one radical Step 2

Step 3: Solve the resulting equation

Equation with one radical Step 3

Step 4: Check all solutions

Let's check to see if x1 = 3 is solution:

Equation with one radical Step 4

Let's check to see if x2 = -1 is solution:

Equation with one radical Step 4

So, the original equation had a single solution x = 3 .

Exercise 1: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

Example 2: Solve Equation with one radical

Solution

Equation with one radical

Let's check it to see if x = 1 is a solution to the original equation.

Equation with one radical

So, the original equation had no solutions.

Exercise 2: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4

Equations with two radicals

Example 3: Solve Equations with two radicals

Solution

First thing to do is get one of the square roots by itself.

Equations with two radicals

We have managed to eliminate one of square roots!! We will continue to work this problem as we did in the previous examples.

Equations with two radicals

Let's check both possible solutions. We will start with x = 0.

Equations with two radicals

Now let's check x = 4.

Equations with two radicals

Exercise 3: Solve equations

Level 1

Exercise 1 answer 1
answer 2
answer 3
answer 4

Level 2

Exercise 2 answer 1
answer 2
answer 3
answer 4