Jim Smith JCHSJim Smith JCHS

Perfect SquaresPerfect SquaresIf You Multiply A Number By It’sIf You Multiply A Number By It’sSelf, You Get A Perfect Square Self, You Get A Perfect Square

1x1 = 1x1 = 112x2 = 2x2 = 443x3 = 3x3 = 99

1, 4, 9, 16, 25, 36, 49, 64, 81, 100,1, 4, 9, 16, 25, 36, 49, 64, 81, 100,121, 144, 169, 196, 225, 256, 289,121, 144, 169, 196, 225, 256, 289,

324, 361, 400324, 361, 400

RadicalsRadicals

This Is A Radical Sign Or A Square RootThis Is A Radical Sign Or A Square RootSymbol. It Means “The Number YouSymbol. It Means “The Number You

Multiply By It’s Self To Get The NumberMultiply By It’s Self To Get The NumberUnder The Sign”.Under The Sign”.

2525 = Radical 25,= Radical 25,

The Square Root Of 25,The Square Root Of 25,

Or The Number You MultiplyOr The Number You Multiply

By It’s Self To Get 25 By It’s Self To Get 25

55++--

2525

Positive rootPositive root

= 5= 5

- 25- 25

Negative rootNegative root

= -5= -5

2525

BothBoth

= -5, 5= -5, 5++--

Which Sign To Use ??Which Sign To Use ??

3636

8181

144144

99

= 6= 6

= 9= 9

= 12= 12

= 3= 3

Never Leave A Perfect Never Leave A Perfect SquareSquare

Under A Radical SignUnder A Radical Sign

3 x 2 x 5 x 7 =3 x 2 x 5 x 7 =

When Multiplying Or DividingWhen Multiplying Or Dividing

Remember:Remember:Whole Numbers ( Rational Whole Numbers ( Rational

Numbers ) With Whole Numbers Numbers ) With Whole Numbers And Radicals With Radicals.And Radicals With Radicals.

3 5 x 2 7 = 3 5 x 2 7 =

6 356 35

5 55 5

10 1510 15

Whole Numbers ( Rational Whole Numbers ( Rational Numbers ) With Whole Numbers Numbers ) With Whole Numbers

And Radicals With Radicals.And Radicals With Radicals.

2 32 3

55

11

55

11

5 55 5

11==

= 2 10= 2 10

Never Leave A Number Under Never Leave A Number Under A Radical Sign That Has A A Radical Sign That Has A

Perfect Square As A Factor.Perfect Square As A Factor.

ab = a x b ab = a x b

= 5 2= 5 2

4040 == 44 1010xx

5050 2525 22== xx

Divide Your Number By 2 And CheckDivide Your Number By 2 And CheckThe Perfect Squares From The Perfect Squares From

That Point Down To 4.That Point Down To 4.

240240

240 / 2 = 120, So Check 240 / 100,240 / 2 = 120, So Check 240 / 100,

240 / 81 Etc. Until You Get A240 / 81 Etc. Until You Get A

Whole Number As An Answer.Whole Number As An Answer.

240 / 16 = 15 So….240 / 16 = 15 So….

= 16 x 15= 16 x 15 = 4 15= 4 15

Never Leave A FractionNever Leave A FractionUnder A Radical SignUnder A Radical Sign

3344

====

====

3344

3322

Never Leave A Radical In The Never Leave A Radical In The Denominator Of A FractionDenominator Of A Fraction

To Simplify This Expression We To Simplify This Expression We RationalizeRationalize

The Denominator. Multiply The The Denominator. Multiply The Denominator By Something That Gives Denominator By Something That Gives

Us A Rational Us A Rational Answer. We Can Usually Multiply It By Answer. We Can Usually Multiply It By

It’s It’s Self. Multiply The Top By The Same Self. Multiply The Top By The Same

Thing.Thing.

33

55==

33 55

55

55

55

xx

xx

22 55 33

xxxx

3333

====

22 1515 33

====

5 65 62 72 7

xxxx

7777

55 4242 2x72x7

====

55 4242 1414