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• SIMPLIFYING 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”.
• The Square Root Of 25,
• Or The Number You Multiply
• By It’s Self To Get 25
• 5
+ -
• Which Sign To Use ?? 25 Positive root = 5 - 25 Negative root = -5 25 Both = -5, 5 + -
• 36 81 144 9 = 6 = 9 = 12 = 3 Never Leave A Perfect Square Under A Radical Sign
• 3 x 2 x 5 x 7 = When Multiplying Or Dividing Remember: Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 6 35 3 5 x 2 7 =
• 5 5 10 15 Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 2 3 5 1 5 1 5 5 1 =
• = 2 10 Never Leave A Number Under A Radical Sign That Has A Perfect Square As A Factor. = 5 2 40 = 4 10 x 50 25 2 = x ab = a x b
• Divide Your Number By 2 And Check The Perfect Squares From That Point Down To 4. 240 240 / 2 = 120, So Check 240 / 100, 240 / 81 Etc. Until You Get A Whole Number As An Answer. 240 / 16 = 15 So…. = 16 x 15 = 4 15
• Never Leave A Fraction Under A Radical Sign 3 4 = = = = 3 4 3 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 5 =
• 5
• 5
5 5 x x
• 5
• 3
= = 5 6 2 7
• 42
• 2x7
= =
• 42
• 14
x x 3 3 = =
• 15
• 3
x x 7 7