Radical Functions: Roots and Properties of Exponents

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Before we begin working with exponents, go back and review taking square roots of numbers.

The first thing we need to go over is perfect squares. If you think in terms of shapes, a perfect square has the same length as width and an area that is (side)2. For example, 12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25, and so on. These are great because working backward allows us to take square roots easily.

square root of one equals 1, square root of four equals 2, square root of nine equals 3, square root of sixteen equals 4, square root of twenty five equals 5...

Sometimes it takes a little more work to find square roots. For example, what if we want to find the square root of 12. The first thing to do is write 12 using as many perfect squares as possible.

square root of twelve equals square root of four times three

We know that square root of four equals 2 and 3 is not a perfect square. If you use your calculator square root of three is approximately one and seventy three hundtredths which is just an approximation. We want to deal with an exact number so we are going to leave square root of three as is. This makes the final answer:

square root of twelve equals two times square root of three

Practice some more square roots with the following worksheet:

Square Root Worksheet

When you are finished, click on "Answer Key" at the bottom of the web page to check your answers. Please note that some square roots can't be simplified anymore because they don't involve any perfect squares.