Here are the steps required for Finding the Domain of a Square Root Function:

Step 1: Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.
Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.
Step 3: Write the answer using interval notation.

Example 1 – Find the Domain of the Function: Example 1

Step 1: Set the expression inside the square root greater than or equal to zero.
Step 1
Step 2: Solve the equation found in step 1.
Step 2
Step 3: Write the answer using interval notation.
Step 3

Example 2 – Find the Domain of the Function: Example 2

Step 1: Set the expression inside the square root greater than or equal to zero.
Step 1
Step 2: Solve the equation found in step 1.
Step 2
Step 3: Write the answer using interval notation.
Step 3

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Example 3 – Find the Domain of the Function: Example 3

Step 1: Set the expression inside the square root greater than or equal to zero.
Step 1
Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol.
Step 2
Step 3: Write the answer using interval notation.
Step 3

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Example 4 – Find the Domain of the Function: Example 4

Step 1: Set the expression inside the square root greater than or equal to zero.
Step 1
Step 2: Solve the equation found in step 1.
Step 2
Step 3: Write the answer using interval notation.
Step 3

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Example 5 – Find the Domain of the Function: Example 5

Step 1: Set the expression inside the square root greater than or equal to zero.
Step 1
Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol.
Step 2
Step 3: Write the answer using interval notation.
Step 3

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