Guided Notes: Radicals

SOL A1.3

Name______Date______


A number is a PERFECT SQUARE if ______
______

First 12 Perfect Squares:
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.

VARIABLES MULTIPLIED
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 ______
______

First 5 Perfect CUBES and Perfect CUBES Variables
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_____=