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SIMPLIFYING RADICALS

Learn how to simplify radicals using perfect squares. A radical sign indicates square roots and multiplying by itself. Remember never to leave perfect squares under a radical sign or fraction. Follow the steps to rationalize denominators for simplified expressions. Practice with examples like √25 = 5 and multiplying numbers with radicals.

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SIMPLIFYING RADICALS

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  1. SIMPLIFYING RADICALS Jim Smith JCHS

  2. 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

  3. 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”.

  4. = Radical 25, • The Square Root Of 25, • Or The Number You Multiply • By It’s Self To Get 25 • 5 + -

  5. Positive root 25 = 5 Negative root - 25 = -5 Both = -5, 5 25 + - Which Sign To Use ??

  6. Never Leave A Perfect Square Under A Radical Sign = 6 = 9 = 12 = 3 36 81 144 9

  7. 3 5 x 2 7 = When Multiplying Or Dividing Remember: Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 3 x 2 x 5 x 7 = 6 35

  8. Whole Numbers ( Rational Numbers ) With Whole Numbers And Radicals With Radicals. 10 15 5 5 2 3 1 1 5 5 5 5 = 1

  9. Never Leave A Number Under A Radical Sign That Has A Perfect Square As A Factor. ab = a x b = = 2 10 40 4 10 x 25 50 2 = x = 5 2

  10. Divide Your Number By 2 And Check The Perfect Squares From That Point Down To 4. = 4 15 = 16 x 15 240 240 / 2 = 120, So Check 240 / 100, 240 / 81 Etc. Until You Get A Whole Number As An Answer. 240 / 16 = 15 So….

  11. Never Leave A Fraction Under A Radical Sign = = = = 3 4 3 4 3 2

  12. 5 5 3 5 • 5 • 5 x x = 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.

  13. x x x x 3 3 7 7 = = • 15 • 3 • 5 • 3 = = = = • 42 • 14 5 6 2 7 • 42 • 2x7

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