Question

07. Rationalize the denominator: 1÷2 root5 -root3​

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{\frac{2 \sqrt{5} + \sqrt{3} }{17} }}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION}}}}}$

$\frac{1}{2 \sqrt{5} - \sqrt{3} } \\ we \: have \: to \: rationlise \: the \: denominator \\ = ) \frac{1}{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \\ = ) \frac{2 \sqrt{5} + \sqrt{3} }{(2 \sqrt{5})^{2} - (\sqrt{3} )^{2} } \\ = ) \frac{2 \sqrt{5} + \sqrt{3} }{4 \times 5 - 3} \\ = ) \frac{2 \sqrt{5} + \sqrt{3} }{20 - 3} \\ = ) \frac{2 \sqrt{5} + \sqrt{3} }{17}$

$\huge{\boxed{\boxed{\sf{\frac{2 \sqrt{5} + \sqrt{3} }{17} }}}}$