Square Roots
A square root is the side length hiding inside an area.
Pick a perfect-square area. The visual builds a square from unit tiles, then marks the side length on the number line.
√4 = 2
A 2 by 2 square has 4 units.
√25 = 5
A 5 by 5 square has 25 units.
√81 = 9
A 9 by 9 square has 81 units.
Build the square
square root
√36 = 6
6 units
Area
36
Side x side
6 x 6
Side length
6
Because 6 x 6 = 36, the square root of 36 is 6.
Break apart √(30z^2)
one box
a
x
b
two boxes
x
a
b
one box
a
+
b
no split
√a + √b
30
x
z
x
z
not a square
√30 stays inside
matched pair
one side length
|z|
result
√(30z^2) = |z|√30