7 Math Vocabulary # 8 (Numerical Roots and Radicals).notebook
7th Grade Math Vocabulary
Numerical Roots & Radicals
Ahrens
Power
A power is another name for an exponent. It is a small, raised number that shows how many times to multiply the base by itself.
Power
3
2
3 x 32
2
3 = x 3 3 33 x 33
2
Base
"3 to the second power"
33 = x x 33 3
Numerical Roots and Radicals Glossary
Power
Exponent
Power of 10
Any integer powers of the number ten. (Ten is the base, the exponent is the power.
A number that shows you how many times to use the number in a multiplication. A quick way to write repeated multiplication.
a.k.a. 10 =
1
=
10 10
10x10 =
10x10x10 =
3
ten to the power of 3
Power 10 = 1,000
2
10 =100
103 =
or What is 72?
Index 7x7 = 49
1
2
10 x 10 x 10 =
1
2
3
1,000
72 = 49
Power of 10
Exponent
Base
Squared
The number that is going to be raised to a power.
A number multiplied by itself once.
Exponent
3
2
Base
"3 to the second power"
2
3 x 32
2
3
= x 3 3 3 3 x 33
3
2
3 = 3x3= 9
3 = x x 333
Base
Squared
1
7 Math Vocabulary # 8 (Numerical Roots and Radicals).notebook
Ahrens
Cubed
Standard Form
A number multiplied by itself twice.
A general term meaning "the way most commonly written"
2
33= 3x3x3
=
3
27
9
=
standard form
4
2 x 3
= 2x2x2x2x3
= 48
y y 3
2
= 9y2
standard form
standard form
Cubed
Standard Form
Expanded Notation
Exponential Form
Writing a number to show each factor that creates the product.
Writing a number using exponents, instead of repeating factors.
4
48
4
= 2 x 3
3 = 3 3 3 3
y3= y y y
3 = 32
3 x 2 x 2 x 3
2
2
3
= 3 x 5
= 2 x 3
= 2x2x2x2x3
Expanded Notation
Exponential Form
Area
Radicand The value inside
the radical sign.
3x3x5x5x5
The number of square units
needed to cover a figure.
The value you want to take the root of.
4 units
3
4
9 = 3
29 = 5.3851... 5
6
7
8
9
10 11 12
144 = 12
13 14 15 16
Area = 16 square units 4 units
4 units
2
1
Area = (4 units)2 Area = 16 units2 Area = 4 units x 4 units Area = 16 square units Radicand
Area
2
7 Math Vocabulary # 8 (Numerical Roots and Radicals).notebook
Square
To multiply a number by itself.
Perfect Square
The product of two equal factors.
What is 4
squared?
What is 10
squared?
4 =
2 What is the square of 6?
4 x 4 = (4)(4) =
16
Ahrens
10 =
2 10 x 10 = (10)(10)=
62 =
100
6 x 6 = (6)(6) =
A number made by squaring a whole number.
49
24
49 = 7
169
(7)(7) = 49 24 = 4.89897...
169 = 13
4.89897... = whole number
(13)(13) = 169 36
Square
Perfect Square
Cube
Square Root
A value that, when multiplied by itself,
gives the number.
The result of undoing the squaring
of a number.
Symbol:
121 = 11
To multiply a number by itself and then again by itself.
What is 4
cubed?
4 =
3 64 = 8
"radical sign"
(8)(8) = 64
8 x 8 = 64
(11)(11) =121
11x11 = 121
The product of three equal factors.
4 x 4 x 4 = (4)(4)(4) =
64
What is 10
cubed?
What is the
cube of 6?
63 =
6 x 6 x 6 = (6)(6)(6) =
103 =
10 x 10 x 10 = (10)(10)(10) =
1000
216
Square Root
Cube
Cube Root
Rational
A value that, when used in a multiplication
three times, gives that number.
Symbol:
3
216 = 6 3
3
64 = 4
"cube root"
(4)(4)(4) = 64
4x4x4 = 64
Cube Root
(6)(6)(6) = 216
6x6x6 = 216
Any number that
can be made by dividing one integer by another.
102
9
rational
(32 = 9)
perfect square
The radical of a perfect square.
81
rational
rational
102 = perfect square
(92 = 81)
perfect square
Rational
3
7 Math Vocabulary # 8 (Numerical Roots and Radicals).notebook
Ahrens
Irrational
The radical of
a non perfect
square.
The decimal form of a number that goes on forever without repeating.
29
irrational
29 = perfect square
16
40
irrational
irrational
(42 = 16)
perfect square
40 = perfect square
Irrational
4