Simplifying square roots 2

The  exercise appears under the Pre-algebra Math Mission. This exercise simplifies the square roots of numbers that are not always perfect squares.

Types of Problems
There is one type of problem in this exercise:


 * 1) Simplify the radical: This problem asks the student to simplify the square root of a natural number by pulling out all the numbers that have powers greater than one in the prime factorization of the integer.Ssr2-1.png

Strategies
Knowledge of prime factorization and how it relates to simplifying radicals would ensure success on this exercise.
 * 1) If one finds the factor tree of the number in the square root, pairs escape the square root and singles will remain. Numbers that meet up on the outside or inside are multiplied.
 * 2) There are sometimes numbers outside the radical initially on this exercise.
 * 3) If there are no numbers inside or outside of the simplified radical these can either be left blank or filled with one on this manipulative.

Real-life Applications

 * 1) Square roots come up in the quadratic formula which models many physical situations, such as acceleration due to gravity.
 * 2) Square roots come up in applications of the Pythagorean Theorem which leads to trigonometry.