Download Squares and Square Roots

Adapted by Debra Garay
Square Root
A number that is multiplied by
itself to form a product is called a
square root of that product.
Taking the square root of a
nonnegative number is the inverse
of squaring the number.
2
6 = 36
√36 = 6
Square Roots
 Every positive number has two square
roots, one positive and one negative.
 The radical symbol √ indicates the
nonnegative or principal square root.
 The symbol -√ is used to indicate the
negative square root.
2
 √16 = 4
4 =16
 -√16 = -4
(-4)2 = 16
You can use the plus or minus
symbol, ±, to indicate both square
roots.
±√16 = ±4
Squares
Squaring a number means finding the area
of a square with that side length.
3
3
3x3=9
√9 = 3
Perfect Squares
A number is a perfect square if
you could take that many 1 × 1 unit
squares and form them into a
square. The sides lengths of the
square you form is that number’s
square root.
Perfect Squares
The numbers 16, 36, and 49 are
examples of perfect squares.
A perfect square is a number that
has integers as its square roots.
Let’s use connecting cubes to find
perfect squares!
Perfect Squares
Create a list of the first 15 perfect
squares.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,
144, 169, 196, and 225.
Caution!
√-49 is not the same as -√49.
A negative number has no real square
roots.
Perfect Cubes and Cube Roots
 Remember
A cube is a three dimensional prism with 6
square faces; so all sides are congruent and
all angles are right angles.
Perfect Cubes
 A number is a perfect cube if you
could take that many 1 × 1 × 1 unit
cubes and form them into a cube. The
sides lengths of the cube you form is
that number’s cube root.
Cubes
Cubing a number means finding the volume
of a cube with that side length.
3
3
3
3 x 3 x 3 = 27
3√27 = 3
Let’s use connecting cubes to find
perfect cubes!
Cube Root
A cube root of a number is a
number when multiply three times,
gives that number.
Taking the cube root of a
nonnegative number is the inverse
of cubing the number.
3√8 = 2
23 = 8
Now it is your turn to practice!
I will hold up a flash card and you have
to solve the problem on it.