RATIONALIZING THE DENOMINATOR USING CONJUGATES

Let (√x + √y) be the denominator of a fraction.

To rationalize the denominator (√x + √y), multiply both numerator and denominator of the fraction by the conjugate (√x - √y) and simplify.

(√x + √y) and (√x - √y) are conjugate to each other.

To multiply (√x + √y) and (√x - √y), the following algebraic identity can be used.

(a + b)(a - b) = a² - b²

Product of (√x + √y) and (√x - √y) :

(√x + √y)(√x - √y) = (√x)² - (√y)²

(√x + √y)(√x - √y) = x - y

Rationalize the denominator in each of the following.

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Example 9 :

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Example 10 :

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