Square Roots Help
Previously you learned how to square a number. For example, 7 2 = 7 × 7 = 49 and 3 2 = 3 × 3 = 9. The opposite of squaring a number is taking the square root of a number. The radical sign is used to indicate the square root of a number, so because 4 2 = 16 and = 5 because 5 2 = 25.
Numbers such as 1, 4, 9, 16, 25, 36, 49, etc., are called perfect squares because their square roots are rational numbers.
The square roots of other numbers such as , , , etc., are called irrational numbers because their square roots are infinite, non-repeating decimals. For example and In other words, the decimal value of cannot be found exactly.
Math Note: The easiest way to find the square root of a number is to use a calculator. However, the square root of a perfect square can be found by guessing and then squaring the answer to see if it is correct. For example, to find , you could guess it is 12. Then square 12. 12 2 = 144. This is too small. Try 13. 13 2 = 169. This is still too small, so try 14. 14 2 = 196. Hence, .
The set of numbers which consists of the rational numbers and the irrational numbers is called the real numbers.
Practice problems for these concepts can be found at: Informal Geometry Practice Test.
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