Square Roots Help

Square Roots

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.

Irrational 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, .

Real Numbers

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.