Download Radicals

Jim Smith JCHS
Perfect Squares
If You Multiply A Number By It’s
Self, You Get A Perfect Square
1x1 = 1
2x2 = 4
3x3 = 9
1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
121, 144, 169, 196, 225, 256, 289,
324, 361, 400
Radicals
This Is A Radical Sign Or A Square Root
Symbol. It Means “The Number You
Multiply By It’s Self To Get The Number
Under The Sign”.
25 = Radical 25,
The Square Root Of 25,
Or The Number You Multiply
By It’s Self To Get 25
+
-
5
Which Sign To Use ??
Positive root
25 = 5
Negative root
- 25 = -5
Both
+
- 25 = -5, 5
Never Leave A Perfect Square
Under A Radical Sign
36 = 6
81 = 9
144 = 12
9
= 3
When Multiplying Or Dividing
Remember:
Whole Numbers ( Rational Numbers )
With Whole Numbers
And Radicals With Radicals.
3 5 x 2 7 =
3 x 2 x 5 x 7 =
6 35
Whole Numbers ( Rational Numbers )
With Whole Numbers
And Radicals With Radicals.
5
10 15
5
1
2
1
3
5
5
1
=
5 5
Never Leave A Number Under A
Radical Sign That Has A
Perfect Square As A Factor.
ab =
40 =
50 =
a x
b
4 x 10 = 2 10
25 x
2 = 5 2
Divide Your Number By 2 And Check
The Perfect Squares From
That Point Down To 4.
240 = 16 x 15 = 4 15
240 / 2 = 120, So Check 240 / 100,
240 / 81 Etc. Until You Get A
Whole Number As An Answer.
240 / 16 = 15 So….
Never Leave A Fraction
Under A Radical Sign
3 =
4 =
3 = 3
4 = 2
Never Leave A Radical In The
Denominator Of A Fraction
To Simplify This Expression We Rationalize
The Denominator. Multiply The Denominator
By Something That Gives Us A Rational
Answer. We Can Usually Multiply It By It’s
Self. Multiply The Top By The Same Thing.
3
x
5
5
x
5
=
3 5
5
2 5 x 3 = 2 15
3 x 3 = 3
5 6 x 7 = 5 42 = 5 42
2 7 x 7 = 2x7 = 14