Question

3 divided by underroot 48 minus underroot 75 is equal to? ​

Answer 1

Step-by-step explanation:

$\frac{3}{ \sqrt{48} - \sqrt{75} } \\ = \frac{3}{ \sqrt{2 \times 2 \times 2 \times 2 \times 3} - \sqrt{5 \times 5 \times 3} } \\ = \frac{3}{2 \times 2 \sqrt{3} - 5 \sqrt{3} } \\ = \frac{3}{4 \sqrt{3} -5 \sqrt{3} } \\ = \frac{3}{ - \sqrt{3} } \\ = - \frac{3}{ \sqrt{3} }$

On rationalizing the denominator we get,

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