1. Simplifying Radicals

2. You’ve already done some work with radicals and square roots such as: Finding the square root of perfect squares Estimate the square root of imperfect squares Compare & order values of roots on a number line

3. You’ve already done some work with radicals and square roots such as: Finding the square root of perfect squares Estimate the square root of imperfect squares Compare & order values of roots on a number line Although this is an important skill to figure out the decimal approximation of a number, there is another skill in which you simplify the radical. To do this, you need to think of factors of the radicand and have one of them be a perfect square.

4. Example 1: Simplify Rewrite the radicand so it is a pair of factors, one of which is a perfect square. You can split them up and write them under their own radical Find the square root of the perfect square, and leave the other one under the radical. Repeat if necessary until you cannot factor the radicand into a perfect square and another number

5. Example 2: Simplify Rewrite the radicand so it is a pair of factors, one of which is a perfect square. You can split them up and write them under their own radical Find the square root of the perfect square, and leave the other one under the radical. Repeat if necessary until you cannot factor the radicand into a perfect square and another number

6. You can use a factor tree, too. 4 240 60 22 4 15 2235 Look at the final factors in your prime factorization. If a number occurs in a pair of two, write one of them outside of the radical, and cross of the other one. Ones that do not occur in pairs get written under the radical. Example 3)

7. You can use a factor tree, too. 4 240 60 22 4 15 2235 Look at the final factors in your prime factorization. If a number occurs in a pair of two, write one of them outside of the radical, and cross of the other one. Ones that do not occur in pairs get written under the radical. Example 3)

8. You can use a factor tree, too. 36 360 10 66 2 5 Look at the final factors in your prime factorization. If a number occurs in a pair of two, write one of them outside of the radical, and cross of the other one. Ones that do not occur in pairs get written under the radical. 2 233 Example 4)

9. You can use a factor tree, too. 36 360 10 66 2 5 Look at the final factors in your prime factorization. If a number occurs in a pair of two, write one of them outside of the radical, and cross of the other one. Ones that do not occur in pairs get written under the radical. 2 233 Example 4)

10. Can you find the number that would have been under the radical if you were given the simplified answer? This problem seems complicated because of the radical symbol. Think about an easier problem to decide how you could solve it. Think of perfect squares first. What would be the answer if I asked: 4 is the square root of what number? 16 because 4x4 =16 Or 10 is the square root of what number? 100 because 10x10 =100

11. Can you find the number that would have been under the radical if you were given the simplified answer? You can find this by squaring what you were given

12. Can you find the number that would have been under the radical if you were given the simplified answer? You can use your calculator to check your answer. The square root of 192 is an irrational number that does not stop or repeat when written as a a decimal. On your calculator you get Compare that to the answer you get if you multiply 8 times the square root of 3. This answer seems reasonable since 13 2 = 169 and 14 2 = 196. The square root of 192 would be a little less than 14.