Question

Rationalizing factor of the expression 1/2+√7 is​

Answer 1

How to Rationalise:-

• First change the sign of denominator.
• Then, after changing sign multiply whole denominator to numerator as well as to denominator.
• Then solve it further by using identities.

SolutioN:-

$⇢ \frac{1}{2 +\sqrt{7} }$

$⇢ \frac{1 × (\ 2 - \sqrt{7}) }{(2 + \sqrt{7} ) \times (2 - \sqrt{7}) }$

$⇢ \frac{2 - \sqrt{7} }{ {(2)}^{2} - { (\sqrt{7} )}^{2} }$ -------( By identity)

$⇢ \frac{2 - \sqrt{7} }{4 - 7 }$

$⇢ \frac{2 - \sqrt{7} }{ - 3}$

Hence ,Rationalised

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Identity used:-

✹ (a + b) ( a - b) = (a)² - (b)²

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More identities:-

❖ ( a + b )² = a² + b² +2ab

❖ ( a - b )² = a² + b² - 2ab