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Surds

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Published in: Mathematics
5,660 Views

This PPT Is Specially Designed For White Board.

Bhavya M / Mumbai

2 years of teaching experience

Qualification: B.A (Mumbai University - 2017)

Teaches: Algebra, Commerce Subjects, Mathematics, Statistics

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  1. SURDS: Simplification, Operations and Rationalisation
  2. Quick Revision Simplify:q 72 27 Subtract: 3 20 — 3 80 — 2 45 t must revise!
  3. 3? 20-3?80-2 45
  4. MU Itiplication Of su rds: Find the product of 241 2, 7420 and 432 Step l: Express the surd in its lowest form (simplify the surd). Step 2: Multiply the whole numbers Step 3: Multiply the radicands. Step 4: Write the whole number and radicand together.
  5. MU Itiply the following: (a) x 43 (b) 245 x 643 (c) 446 x 3420 Stepl : Step2: Step3: Ste 104: (d) 7435 x 2498
  6. Division Of su rds: Divide 6442 and 2414. Step l: Express the surds in their lowest forms (simplify the surds). Step 2: Divide the whole numbers Step 3: Divide the radicands. Step 4: Write the whole number and radicand together.
  7. Divide the follow in g: (a) +43 (b) 846 + 243 (c) 4460 + 246 Stepl : Step2: Step3: Ste 104: (d) 7435 x 45
  8. R ation al is ation Of su rds (O)
  9. What do we mean by 'rationalising a SUrd?' Rationalising a surd essentially means eliminating/ deleting a surd from the denominator i.e. making the denominator a rational number. For example: 3 Rationalise: We have to think of such a number which when multiplied by the numerator AND the denominator, makes the denominator a whole number. In our case, the denominator is V2. When V 2 is multiplied to itself, when get 2. (2)1/2 X (2)1/2 Hence, V 2 is the rationalising factor. 3 V2 3V2 2
  10. Therefore, steps to rationalise a surd are: 1. Find the rationalising factor. (A rationalising factor is the one which when multiplied to BOTH numerator and denominator, makes the denominator a whole number) 2. Multiply the numerator and denominator with the rationalising factor. 3. Write the resulting numerator and denominator. 4. Simplify the new fraction to its lowest form.
  11. DO Now: Find the rationalising factor of the following surds: ' 3V3 2V5 ' 3V6
  12. Let us now try a slightly different problem. 1 Rationalise: 3-V5 Steps of rationalisation remain the same here. We first need to find a rationalising factor. Take 2 mins and think of a suitable rationalising factor.
  13. Exam ple 2: 5 Rationalise Stepl : 506-2) Step 2: -10 Step 3: —22 -10 Step 4: -10 5Nfi step 5: -1 (Using the identity (a+b)(a-b)=a
  14. R ation alise the follow in g: 2 1. MS-I 4 7 3. 1 4. 2-V7 5 V 3-1

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