square root

Test Tip Even though finding perfect squares is easily done on a calculator, don't fall into the calculator trap! You will be much more efficient if you are able to recognize and use perfect squares without a calculator. While this is not an exhaustive list, it will be extremely helpful for you to memorize this list. Your work will go much more quickly if you can recognize a number as being a perfect square. Just keep in mind that this list continues forever!

1 2 = 1 6 2 = 36 11 2 = 121 2 2 = 4 7 2 = 49 12 2 = 144 3 2 = 9 8 2 = 64 13 2 = 169 4 2 = 16 9 2 = 81 14 2 = 196 5 2 = 25 10 2 = 100 15 2 = 225

Perfect Squares: rational number

A number that can be squared to get an answer. or a number that when multipled by itself can get an rational answer

irrational numbers.

As we continue to break into smaller units, our numbers will continue to get closer to 20 but will never quite reach it. In fact, even if we kept breaking the numbers down forever, we would never reach the exact number 20. That's because square roots of numbers that are not perfect squares are always irrational numbers. or in this case a number where you cant find the root of but make a estimate like theres no square root of 56 but the closest would be 7 or 8

Connections

Do you remember from the clip at the beginning of the lesson why these are called perfect squares? Draw a square that is 3 inches by 3 inches. What is the area of this square? How did you find the area?

simplifying square roots

Example (continued) √8 = √(4×2) = √4 × √2 = 2√2To simplify a square root: make the number inside the square root as small as possible (but still a whole number):

warning

Finding the square root of a number is not the same as dividing a number by two. Just like squaring a number is not the same as multiplying a number by two. Squaring a number means to multiply a number by itself, and the square root of a number tells you what number was multiplied by itself.

square root

a number that when multiplied by itself (squared) equals a given number

irrational number

a number which, when in decimal form, does not terminate or repeat

perfect square

any rational number that is the square of another rational number

SQUARE ROOTS AND PERFECT SQUARES The square root symbol

is used to ask the question, "What number squared is ...?" For example, , read as "the square root of 36," means to find a number that when squared equals 36