This week in Pre Calculus 11, I learned how to solve radical equations. It was a little bit difficult for me at some points, because I didn’t understand squaring. Today I will teach you how to deal with these kinds of expressions.

Steps:

- Solving
- Restrictions
- Checking

Example

= 6

SOLVING

- remove the radical sign by squaring both sides of the equation.

=

- Simplify

x = 36

Restrictions

Note: a number under a radical sign can not be negative because a number times itself is positive weather it be -x or x. The only exception is if it has a odd power.

In the example above x needs to be a positive number so its restriction would be x > 0 or x = 0.

Check It Out

- = 6
- 6 = 6

This is how to solve a basic radical equation. Now I will move on to a more difficult equation to maximize your understanding.

Example 2

1 = -3

Note: When solving eq, what you do to one side you have to do to the other.

SOLVING

- Place the constants on side of the equation

- 1 + 3 =
~~-3 + 3~~ - 4 =

2. Combine the radical terms

Note: The radicans are the same so they can be combined together. Place them on one side of the equation.

- 4 =
- 4 + = +
- 4 =

3. Square both sides to remove the radical sign.

- =
- = 2x
- 16 = 2x

4. Isolate x

- =
- = x
- 8 = x

RESTRICTIONS

x > 0 or x = 0

Check It Out

- 1 – = -3 –
- 1 – = -3 –
- 1 – = -3 –
- 1 – 12 = -3 – 8
- -11 = -11

This is how you solve radical equations.

Comment below if this helped you or if you have any questions. 🙂