This week in Pre-calculus 11 we learned about radical expressions and how you would solve them. We learned that in order for you to solve a radical expression you must understand that square roots and squaring are inverse operations. Inverse operations are opposite operations. ex. addition is the opposite of subtraction.

Before solving a radical expression, you must recall:

• What you do to one side you must do to the other
• You need to isolate in order to get a variable by itself
•  When you divide by a negative number in a inequality you have to flip the sign (this is only important when you are writing your restrictions)

Note: when writing your restrictions you must write whatever is under the square root sign and isolate to find the restrictions for x.

ex.   = 2

Restriction:

• 2x+6 ≥ 0
• 2x ≥ -6
• x ≥ -3

Example:

  

1. First, we need to get rid of the sign. In order to do this we put brackets around it and square it. Since we square the left side we need to square the right side as well.
2. In the expression x is already isolated we don’t need to move anything around; x = 36.
3. Since all expressions involve variables, after finding a value for x we need to write a restriction. Since it is a square root x needs to be greater than or equal to zero, x  ≥ 0. We then double check that our value for x fits into our restriction.
4. After solving for x and making a restriction you then need to do a check to make sure that you got the correct value for x. All you do is input your value for x into the expression and solve it. Both sides need to equal the same number, if not, you need to go back and double check that you solved the expression correctly.

The steps for solving an expression are:

1. Solve for x
2. Write a restriction
3. Check

Example:

  

1. Since there is a coefficient of 4 in front of the ,we divide both the left and right side by 4. By doing this it makes the expression easier for us to solve. .
2. We then square both sides to get rid of the .
3. Since we have found the value of x, we need to write a restriction. Since it is a square root x needs to be greater than or equal to zero, x  ≥ 0. Check that your value for x fits into the restriction.
4. Check.

Similar Example:

  

Example:

• Sometimes there will be instances where there is No Solution to the expression. These expressions are referred to as Extraneous Solutions. You will be able to tell if an expression is an extraneous solution if the square root in a question is equal to a negative number. The reason that this type of expression will have no solution is because it isn’t a true root. No square root should be equal to a negative number just like how you can’t have a negative number as the radicand.
• If you come across an expression where the square root is equal to a negative number, simply write no solution.