Guided Notes: Radicals
SOL A1.3
Name______Date______
A number is a PERFECT SQUARE if ______
______
NUMBER MULTIPLIED
BY ITSELF / PERFECT SQUARES / NUMBER MULTIPLIED
BY ITSELF / PERFECT SQUARES
1 X 1 = / ______/ 7 X 7 = / ______
2 X 2 = / ______/ 8 X 8 = / ______
3 X 3 = / ______/ 9 X 9 = / ______
4 X 4 = / ______/ 10 X 10 = / ______
5 X 5 = / ______/ 11 X 11 = / ______
6 X 6 = / ______/ 12 X 12 = / ______
A variable is a perfect square if it has an ______exponent.
BY ITSELF / PERFECT SQUARES
x∙x= / ______
x2∙x2= / ______
x3∙x3= / ______
x4∙x4= / ______
Taking the square root of a number is the ______
______
For example if 32= ______, then 9=______. The symbol tells you to ______
______
An expression that contains a square root is a ______. It can have three parts.
Simplify the following radical expressions.
100= ______/ x4= ______25= ______/ 4x2=______= ______
141= ______/ 81x8y2=______= ______
x2= ______/ 36a6b4=______= ______
When dealing with exponents, ______to get the exponent of the roots.
If your radicand has more than one factor, ______
Simplify: 24
Since 24 is not a perfect square, its ______. To simplify
this radical, 24 needs to be ______.
However, one of the factors must be a ______.
What is the highest factor of 24 that is also a perfect square? ______. Therefore, 24 = ____ X _____
24=_____∙______=______∙ ______=______
Simplify: 32
What is the highest factor of 32 that is also a perfect square? ______. Therefore, 32 = ____ X _____
32=_____∙______=______∙ ______=______
Simplify: 54
What is the highest factor of 54 that is also a perfect square? ______. Therefore, 54 = ____ X _____
54 =
Simplify: x5
What is the highest factor of x5 that is also a perfect square? ______. Therefore, x5= ____ X _____
x5=_____∙______=______∙ ______=______
Simplify: 50x2y
What’s the highest factor and perfect square of 50x2 ? ______. Therefore, 50x2= ____ X _____
50x2y=_____∙______=______∙ ______=______
Simplify: 42x9
What is the highest factor and perfect square of 42x9 ? ______. Therefore 42x9= ____ X _____
42x9=
A number is a PERFECT CUBE if ______
______
NUMBER MULTIPLIED
BY ITSELF 3 TIMES / PERFECT CUBES / VARIABLE MULTIPLIED
BY ITSELF 3 TIMES / PERFECT CUBES
1 X 1 X 1 = / ______/ x∙x∙x= / ______
2 X 2 X 2 = / ______/ x2∙x2∙x2= / ______
3 X 3 X 3 = / ______/ x3∙x3∙x3= / ______
4 X 4 X 4 = / ______/ A variable is a perfect square if the exponent is ______
______
5 X 5 X 5 = / ______
Taking the cube root of a number is the ______
______
For example if 23= ______, then 38=______. The symbol 3 tells you to ______
______
Simplify the following radical expressions:
3125= ______327= ______
3x3= ______
364x12= ______
Simplify: 354:
What is its highest factor and perfect cube the radicand? ______. Therefore, 54? = ____ X _____
354 =3_____∙______=3_____∙3_____=
Simplify: 324x8:
What is its highest factor and perfect cube of the radicand? ______. Therefore, 24x8? = ____ X _____
324x8 =3_____∙______∙______=3_____∙3_____∙3_____=