Question

express the following with a rational denominator:
• 3/ root 5+ root2​​

Answer 1

Answer:

$\frac{3}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5 } - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \frac{3( \sqrt{5} - \sqrt{2}) }{3} \\ ( \sqrt{5} - \sqrt{2} ) \\ ansssssssssssssssssssssss$

Step-by-step explanation:

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Answer 2

Given

$\dfrac{3}{\sqrt{5}+\sqrt{2} }$

Rationalizing, we get,

$\dfrac{3}{\sqrt{5}+\sqrt{2} } * \dfrac{\sqrt{5} -\sqrt{2} }{\sqrt{5}-\sqrt{2} }$

$\dfrac{3(\sqrt{5}-\sqrt{2} ) }{(\sqrt{5} )^{2} - (\sqrt{2})^{2} }$

$\dfrac{3(\sqrt{5} - \sqrt{2}) }{3}$

$\boxed{\boxed{\bold{\sqrt{5} -\sqrt{2}}}}}}$