Radical Learned

Simplifying Radicals Radical- the square root So simplifying a radical is another way of saying find the square root Some times the square root of a number is a whole number. For example: 49 = 7 But sometimes the square root of a number is not a whole number. When you type in 48 into your calculator, you get 6.92820323. This number is not the exact answer for the 48; it is a DECIMAL APPROXIMATION. Most teacher do not want a decimal approximation, they want the SIMPLIFYED RADICAL FORM. In order to simplify a radical whose answer is not a whole number, you use the factor tree to find out its prime factorization. Ex. 48

16) square multiply all the the number tree that answer inside symbol

If you are finding out the numbers prime factorization and get a perfect square, (in this case we got then find the perfect squares square root and put it in front of the root symbol. Then prime numbers in together and put the square root

WHAT IF YOU GET 2 PERFECT SQUARES WHILE FINDING THE PRIME FACTORIZATION? If you get 2 perfect squares while finding the prime factorization, multiply both their square roots together. Put that number outside off the square root sign, and multiply the prime numbers and put them into the square root sign For example: 34

QUESTION AND ANSWER 1. a 4 = a 2

2.

a 10

= a5

3.

a7 = a 3 a

4.

a 3 =a 2 a

5.

a9 = a4 a

6.

a 15 = a 7 a

7.

4x 3 = 2x x

8.

8x 5 y 6 = 2x 2 y 3 2x