# In the Following Determine Rational Numbers A And B: (4 + Sqrt2)/(2 + Sqrt2) = N - Sqrtb - Mathematics

In the following determine rational numbers a and b:

(4 + sqrt2)/(2 + sqrt2) = n - sqrtb

#### Solution

We know that rationalization factor for 2 + sqrt2 is 2 - sqrt2. We will multiply numerator and denominator of the given expression (4 + sqrt2)/(2 + sqrt2) by 2 - sqrt2 to get

(4 + sqrt2)/(2 + sqrt2) xx (2 -  sqrt2)/(2 - sqrt2) = (4 xx 2 - 4 xx sqrt2 + 2 xx sqrt2 - (sqrt2)^2)/((2)^2 - (sqrt2)^2)

= (8 - 4sqrt2 + 2sqrt2 - 2)/(4 - 2)

= (6 - 2sqrt2)/2

= 3 - sqrt2

On equating rational and irrational terms, we get

a - sqrtb = 3 - sqrt2

Hence we get a = 3, b = 2

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 6.2 | Page 14

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