# Express Each One of the Following with Rational Denominator: (B^2)/(Sqrt(A^2 + B^2) + A) - Mathematics

Express each one of the following with rational denominator:

(b^2)/(sqrt(a^2 + b^2) + a)

#### Solution

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

b^2/(sqrt(a^2 + b^2) + a) xx (sqrt(a^2 + b^2) - a)/(sqrt(a^2 + b^2) - a) = (b^2(sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2) - a^2)

= (b^2 (sqrt(a^2 + b^2) - a))/(a^2 + b^2 - a^2)

= (b^2(sqrt(a^2 + b^2) - a))/b^2

= sqrt(a^2 + b^2) - a

Hence the given expression is simplified with rational denominator to sqrt(a^2 + b^2) - a

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 3.9 | Page 14

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