# In the Following Determine Rational Numbers A And B: (3 + Sqrt2)/(3 - Sqrt2) = a + Bsqrt2 - Mathematics

In the following determine rational numbers a and b:

(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2

#### Solution

We know that rationalization factor for 3 - sqrt2 is 3 + sqrt2. We will multiply numerator and denominator of the given expression (3 + sqrt2)/(3 - sqrt2) by 3 + sqrt2 to get

(3 + sqrt2)/(3 - sqrt2) xx (3 + sqrt2)/(3 + sqrt2) = ((3)^2 + (sqrt2)^2 + 2 xx 3 sqrt2)/((3)^2 - (sqrt2)^2)

= (9 + 2 + 6sqrt2)/(9 - 2)

 = (11 + 6sqrt2)/7

= 11/7 + 6/7 sqrt2

On equating rational and irrational terms, we get

a + bsqrt2 = 11/7 + 6/7 sqrt2

Hence we get a = 11/7, b =  6/7

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 6.3 | Page 14

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