Download Example (negative square root): − 16 = −4•−4

Mathematical Roots
Square Numbers
A square is a shape that has equal side lengths and 4 right angles. To
find the area of a square (space inside), square the length of the sides
(multiply side length side length).
3
Example:
Another Example:
So, “if there is a pair….there is a square”.
3
A perfect square is made from integers (... − 3, −2, −1, 0, 1, 2, 3...) . You should memorize
the following perfect squares in addition to their opposites (like 2 and –2)
Square Roots
To square root a number you have to “undo the square”. The square root of a number is
one of the two equal numbers (factors) that are multiplied together to get the number.
16 = 4 • 4 = 4
Example (positive square root):
Example (negative square root):
Example (both square roots):
Try: ± 25 =
− 16 = −4 • −4 = −4
± 16 = ± 4 • 4 = ±4
± 144 =
−16 =
± x2 =
Square Roots of Fractions
Example:
Try:
81
100
4
2•2 2 1
=
= =
16
4•4 4 2
36
64
Solving Equations with Square Roots
Try: y 2 =
Examples:
4
25
z 2 = 0.09
x 2 = 49
x 2 = 49
x • x = 7• 7
x = 7
Cube Roots
Here we have to “undo” a number that is cubed. A cubed number is a number raised to
the power of 3 or a number multiplied by itself 3 times.
Example 2 • 2 • 2 = 8 (8 is a “perfect cube); “if there is a triple, there is a cube”
The Perfect Cubes (0-10)
03
33
13
23
0
1
8
27
53
125
43
64
63
216
73
343
83
512
When we do a “cube root” we undo a “triple”.
Example
3 64 = 3 4 • 4 • 4 = 4
Try:
3
3
125
Solving Equations with Cube Roots
3
x 3 = 8
3 x 3 = 3 8
3
x• x• x = 3 2•2•2
x = 2
Try: x = 343
−27
93
729
10 3
1000