Pre-Algebra - Introduction to Radicals

If you remember learning the “square root of” problems, when asked to find the square root of say “4”, the answer was “2”. This is because the square root of a number is a number times itself that will give you that beginning number.

As stated above, “4” is the beginning number and 2 times itself (i.e., 2 x 2) equals 4.

However, “2” is not the only square root of “4” as a “-2” times itself also equals “4” because a negative number times a negative number gives you a positive number. So, when asking what is the square root of “4,” the answer can be written as +, -2 (or the plus sign can be placed over the minus sign).

When asked to simplify the square root of 36 (√36), you are being asked to give the “positive” square root, not the negative. Sometimes this would be referred to as the “principal square root.”

When you are asked to give the square root of -√16, you are being asked to give the opposite or negative square root. For example, the square root of 16 is 4 but you are being asked for -√16 which would be -4.

Square root of variables: When finding the square root of a variable (an unknown number) you would have: √x² = x because x times itself gives you x². As another example: √8pq² = 8pq.

Values: Real or Not - To determine if a value of a number is real, it must be a positive number. For example, √36 = 6 which is a real value. However, √-36 is not a real value because no number times itself will give you a negative 36. But, if you have -√36, the value would be a -6 because the question is asking for the opposite of the square root of 36. As the square root of 36 is 6, the opposite is -6.