Question

What are the characteristics of a radical equation?
How is solving radical equations similar to solving linear equations?
Why is it important to check the solutions to a radical equation?
Create your own radical equation. Describe in complete sentences and demonstrate the process in finding its solution(s)
I'm clueless when it comes to this stuff, could anyone help me?

Answer 1

The characteristics of a radical equation:
1. It contains a radical
2. It is solved by raising both sides of the equation to the appropriate power.
3. If the root is an even root, the radicand cannot be negative.
It is important to check the solution because sometimes an extraneous root is introduced during the process of raising both sides to a power.
3. \[\sqrt{x+3}=2\]
Since this is a second root, I will raise both sides to the second power.
\[(\sqrt{x+3})^2=2^2\]
Since raising to the second power is the inverse of extracting the second root, the equation becomes:
\[x+3=4\]
Now complete the solution by subtracting 3 from both sides.
The result is:
\[x=1\]
Now the solution must be checked by replacing x with 1 in the original equation:
\[\sqrt{1+3}=2\]
Since the principal square root of 4 is indeed 2, the answer checks and the solution is x = 1

Answer 2

thanks so much, i know this was probably simple to you but its like greek for me, thanks again!!

Answer 3

yw