Question

Rationalise the denominator:
3√5+√3 /√5-√3​

Answer 1

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Answer 2

Answer:

9 + 2√5

Step-by-step explanation:

Rationalizing the denominator: Converting an irrational denominator of a fraction to a rational denominator.

Given expression:

$= \frac{3 \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

Rationalizing the given expression:

To rationalize, we need to multiply the numerator and denominator by √5 + √3 / √5 + √3.

$= \frac{3 \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$= \frac{(3 \sqrt{5} + \sqrt{3} )( \sqrt{5} + \sqrt{3}) }{( \sqrt{5} - \sqrt{3})( \sqrt{5} + \sqrt{3}) }$

$= \frac{3 \sqrt{5}( \sqrt{5} + \sqrt{3} ) + \sqrt{3}( \sqrt{5} + \sqrt{3} ) }{5 - 3}$

$= \frac{15 + 3 \sqrt{15} + \sqrt{15} + 3 }{2}$

$= \frac{18 + 4 \sqrt{15} }{2}$

$= \frac{2(9 + 2 \sqrt{15}) }{2}$

$= 9 + 2 \sqrt{15}$