Question

rationalize the denominator 2-root 5/2+root 5​

Answer 1

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Q:-rationalize the denominator 2-root 5/2+root 5

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$⟹ \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} }$

$⟹ \frac{( {2 - \sqrt{5} )}^{2} }{ ({2})^{2} - {( \sqrt{5}) }^{2} }$

$⟹ \frac{( {2})^{2} + {( \sqrt{5}) }^{2} - 2(2)( \sqrt{5} ) }{4 - 5}$

$⟹4 + 5 - 4 \sqrt{5} = 9 - 4 \sqrt{5} ✓$

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