## Surds

Published in: Mathematics
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• ### Bhavya M

• Mumbai
• 2 Years of Experience
• Qualification: B.A
• Teaches: Statistics, Mathematics, Commerce Subjects, Algebr...
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This PPT Is Specially Designed For White Board.

• 1
SURDS: Simplification, Operations and Rationalisation
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Quick Revision Simplify:q 72 27 Subtract: 3 20 — 3 80 — 2 45 t must revise!
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3월 20-3월80-2 45
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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.
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MU Itiply the following: (a) x 43 (b) 245 x 643 (c) 446 x 3420 Stepl : Step2: Step3: Ste 104: (d) 7435 x 2498
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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.
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Divide the follow in g: (a) +43 (b) 846 + 243 (c) 4460 + 246 Stepl : Step2: Step3: Ste 104: (d) 7435 x 45
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R ation al is ation Of su rds (O)
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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
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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.
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DO Now: Find the rationalising factor of the following surds: ' 3V3 2V5 ' 3V6
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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.
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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
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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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