1. Honors Geometry Square Root Review

2. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and etc.

3. Formal definition of “the square root of a”: iff _____

4. * Note that since, both 7 and –7 are square roots of 49. In geometry, the square root will represent the length of a segment, which is always positive. Consequently, we will only use the positive square root of a number.

5. Any number whose square root is a whole number, such as the examples above, is called a perfect square. Complete the list of the first 15 perfect squares. 1,4,9,16,25,

6. The square root of any whole number that is not a perfect square will be an irrational number. An irrational number is a number that

7. When an irrational number is written as a decimal, the decimal does not terminate nor repeat.

8. On quizzes and tests, you must always give an exact answer unless you are told to round. If your answer involves a square root, you must always simplify the square root.

9. To simplify a square root, you must “factor out” any perfect square factor (other than 1) in the radicand (the number under the radical sign). When simplifying a square root, that is not a perfect square, you will not eliminate the square root entirely. The goal is to make the radicand as small as possible.

10. Examples: Simplify.

11. What’s wrong with the following simplification? Neither 3 nor 6 is a perfect square.

12. If a problem involves multiplying square roots, you simply multiply the whole numbers and multiply the radicands. You can never multiply a whole number times a radicand.

13. Examples:

15. In the same way that addition is the inverse operation of subtraction and multiplication is the inverse operation of division, taking the square root is the inverse operation of squaring a number.

16. Solve each equation for x. Round your answers to the nearest 1000 th. Technically (like in Algebra II next year), when you introduce the square root into a problem, you must consider both the positive and negative square root that can result. But as I mentioned earlier, here in geometry, we will consider only the positive value.

17. Solve each equation for x. Round your answers to the nearest 1000 th.