Kingman - Semester 2 Review: Unit 5 - Square and Cube Roots

Summary of Knowledge:
The goal for this investigation is to use square roots to find the side lengths of a square using the given area. You know that a square has two same sides and multiply both to give you thre area (x^2 ) (x*x)

Cube roots are important to find the side lengths of a cube by a given area.
Ex: volume : 27
side length: 3
( 3*3*3 = 27)

Key Vocabulary:
Irrational Number: A number in the decimal portion that never ends and does not repeat.
Cube roots: A number that must be multiplied by itself three times to equal a given number.
Ex: 27 the cube roots of 27 is 3 (3*3*3)
Square Roots: A nonnegative numner that must be multiplied by itself to equal a given number.
Ex: 4 the square root of 4 is 2 (2*2)

Task Analysis Square Roots:
1 Numbers should be perfect squares. This means that the product of a number multiplied by itself ( use nultiplication tables to help you know which numbers are square roots.)
2 If a number is not a square number write the two square roots in between.
Ex:
√20 Irrational in between 4 and 5
4*4 =16 5*5=25
20 is in between 16 and 25

Task Analysis of Cube Roots
1: Think of 2 factors that make the number that you are finding the cube roots.

Ex:
∛8
Factors: 2 AND 4

2: Then see if the small number can be used to divide the big number( the answer has to be the same as the small number). Also you can think if the big number is a square number. And of the square root is the small number.

Ex:
∛8 Factors: 2 AND 4
Factors of 4 : 2, 2 (2x2= 4)

3:Then multiply the 3 small numbers and the number should be the cubed number in the beggining.

Ex: 2x2x2 = 8 ( the cubed root of 8= 2)
4:If the number its irrational think of two numbers that are in between the cubed number.
Ex:
∛16
The 2 cube numbers are: 8 and 27
The cube root f 8: 2 (2x2x2) The cube roots of 27 : 3 (3x3x3)
The answer is : irrational in between 2 and 3