Question

3/(√48- √75) is equal to

Answer 1

SOLUTION :

$\frac{3}{ \sqrt{45} \: - \: \sqrt{75} } \\ \\ rationalizing \: the \: denominator \\ \\ = \frac{3}{ \sqrt{45} \: - \: \sqrt{75} } \times \frac{ \sqrt{45} \: + \: \sqrt{75} }{ \sqrt{45} \: + \: \sqrt{75} } \\ \\ = \frac{3( \sqrt{45} \: + \: \sqrt{75} ) }{( \sqrt{45} - \: \sqrt{75})( \sqrt{45} \: + \sqrt{ 75}) } \\ \\ = \frac{3( \sqrt{45} \: + \sqrt{75}) }{( \sqrt{45}) {}^{2} - ( \sqrt{75) {}^{2} } } \\ \\ = \frac{3( \sqrt{45} + \sqrt{75}) }{ - 30}$

Answer 2

Answer:

$-\sqrt{3}$

Step-by-step explanation:

$\frac{3}{\sqrt{48}\ - \sqrt{75} } \ = \frac{3}{\sqrt{2*2*2*2*3} \ -\sqrt{5*5*3} }$

$= \frac{3}{2*2*\sqrt{3}\ - \ 5*\sqrt{3} } \ = \frac{3}{4\sqrt{3} \ - 5\sqrt{3} }$

$= \frac{3}{-\sqrt{3}} \ = \ \frac{-3}{\sqrt{3} } \ = \ -\frac{3}{\sqrt{3} } * \frac{\sqrt{3} }{\sqrt{3} }$

$\frac{-3*\sqrt{3} }{\sqrt{3}*\sqrt{3} } \ = \ \frac{-3\sqrt{3} }{\sqrt{3^{2} } }$

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