1、Square Roots“ “ plus any number equals exponent“ “ equals square root symbolPerfect SquaresTo find a perfect square of a number you take a whole number that is between 1 and 10 and multiply it by itself. Square of n = n2 Square of 5=5x5=52=25The perfect squares are the squares of the whole numbers.P
2、erfect Squares:1 2 3 4 5 6 7 8 9 101 4 9 16 25 36 49 64 81 100Finding Square Roots of Numbers That Arent Perfect Squares Without a CalculatorTo find the square root of a number without using a calculator you must do the following steps:1. Estimate - first, get as close as you can by finding two perf
3、ect square roots your number is between.2. Divide - divide your number by one of those square roots.3. Average - take the average of the result of step 2 and the root.4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.ExampleCalculate the squa
4、re root of 10 (10) to 2 decimal places.1. Find the two perfect square numbers it lies between.Solution:32 = 9 and 42 = 16, so 10 lies between 3 and 4.2. Divide 10 by 3. 10/3 = 3.33 3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667Repeat step 2: 10/3.1667 = 3.1579Repeat step 3: Average 3.1579 and 3.1667.
5、(3.1579 + 3.1667)/2 = 3.1623Check Your Answer - Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001Practice Problems for Solving Square Roots Without Using a CalculatorProblem#1:60Problem#2:7Problem#3:75Problem#4:33Problem#5:66Answer to Problem#1: 7.745Answer to Problem#2: 2.645Answer to Proble
6、m#3: 8.660Answer to Problem#4: 5.744Answer to Problem#5: 8.124 Properties of square rootsSquare roots have the following propertiesa+b = a + bab = a * ba/b = a/ba2 = aAddition and Subtraction of Square RootsAdding and subtracting square roots is just like combining like terms when you need to do tha
7、t with algebraic expressions. If the indices (a square roots index is 2, a cube roots index is 3, a 4th roots index is 4, etc.) or the radicands (the expression under the root sign or enclosed by brackets after the square root) are the same.When adding and subtracting you keep the bases the same and
8、 add or subtract just the co-efficient.Examples42 + 72 = 112123 83 = 4322 52 + 672 = 642Practice Problems Adding and Subtracting Square RootsProblem#1: 9595 + 9595=Problem#2: 56 + 366=Problem#3: 657 237=Problem#4: 3366 + 166 23566=Problem#5: 85432 85532 + 32=Quick SolutionsAnswer to Problem#1: 19095
9、Answer to Problem#2: 416Answer to Problem#3: 427Answer to Problem#4: -20166Answer to Problem#5: 0Multiplication and Division of Square RootsTo multiply a square root equation you multiply all of the co-efficients together and then all of the radicals together.To divide a square root equation you hav
10、e to take the two terms and divide the co-efficients together and then all of the radicals together.Examples2. 259/53=25/5=5=9/3=3=532. 26*622=2*62=124=6*2=1212412Practice Problems for Multiplication and DivisionProblem#1: 64*78=Problem#2: 124/32=Problem#3: 8124/93=Problem#4: 12645*23= Problem#5: 74
11、2=Quick SolutionsAnswer to Problem#1: 4232Answer to Problem#2: 368Answer to Problem#3: 98Answer to Problem#4: 6315Answer to Problem#5: 4916Mini Quiz1. Is 75 a perfect square?2. What is the root of 64?3. 30=4. 52=5. 36 + 46=6. 162 112=7. 227*83=8. 3316/34=9. 1572=10. 832 + 632=Quick Solutions to Mini Quiz1. No2. 83. 5.4774. 7.2115. 766. 527. 176218. 1149. 30710. 1009Websites For Further Informationhttp:/library.thinkquest.org/20991/textonly/alg/roots.html?tqskip1=1&tqtime=0410http:/math.usask.ca/readin/roots.htmlhttp:/
