Question

What reasoning and explanations can be used when solving radical equations?

Answer 1

A good thing to remember when solving radical equations is "get rid of radicals". If possible, square both sides of the equation or multiply by whatever order radicals you have. It is generally easier to solve equations when you don't have radicals

Answer 2

The common reasoning that can be use while solving a radical equation are shown below.

Explanation:

Radical equations are the equations which contains radical expressions like
`√(x)\text{ and }√(x+2)`, etc.

If a radical expression is defined as
`√(x)`, then the sign
`\sqrt{}` is the radical and x is radicand.

The common reasoning that can be use while solving a radical equation are:

1. Isolate or separate the radical expression.

2. To remove radical square both sides of the equation.

3. After that solve the equation to find the unknown variable

4. Check the answer for solution or extraneous solution.

For example:

`√(x+1)+1=x`

subtract 1 from both sides.

`√(x+1)=x-1`

Taking square on both sides.

`x+1=(x-1)^2`

On simplification we get

`x+1=x^2-2x+1`

`0=x^2-2x+1-x-1`

`0=x^2-3x`

`0=x(x-3)`

Using zero product property,

`x=0,x-3=0\Rightarrow x=3`

Check the equation for x=0,

`LHS=√(0+1)+1=1+1=2\\eq 0=RHS`

Since LHS is not equal to RHS, therefore 0 is an extraneous solution.

Check the equation for x=3,

`LHS=√(3+1)+1=2+1=3=RHS`

Since LHS is equal to RHS, therefore 3 is an solution.