Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Simplifying Radicals Section 5.3 Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator Radicals - definitions The definition of x is the number that when multiplied by itself 2 times is x. 4 22 2 16 x x x x 2 Simplifying radicals Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s). The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …. Try these - simplify: If a radical has a perfect square factor, then we can pull it out from under the sign. Ex: 25 5 50 2 2 32 48 x5 72 a 4b 7 98 3 27m3n7 Adding or Subtracting Radicals To add or subtract square roots you must have like radicands (the number under the radical). 2 3 2 4 2 Sometimes you must simplify first: 2 18 2 3 2 4 2 Try These 3 5 5 5 3 75 48 4 5 5 18 3 5 5 5 2 20 3 80 Multiplying Radicals You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce. 2 3 2 3 4 3 2 6 3 5 5 2 15 10 Try these: 2 7 5 (3 12 )( 2 3 ) 2 2 3 5 2 10 2 5 2 Dividing Radicals To divide square roots, divide any whole numbers and then divide the radicals one of two ways: 1) divide the numbers under the radical sign and then take the root, OR 2) take the root and then divide. Be sure to simplify. 20 20 5 5 20 2 5 2 5 5 or 20 4 2 5 Try These 1 4 40 10 100 4 8 14 2 2 100 25 80 10 Rationalizing Radicals It is good practice to eliminate radicals from the denominator of an expression. For example: 3 We need to eliminate 2 2 We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways… Since 2 2 2 we will multiply by one where 1 3 2 2 2 3 2 2 2 3 2 2 2 2 Try These 5 3 2 2 5 3 5 10 5 3 12 2 5 3 8 7 20