Question

6. Simplify by rationalising the denominator.

Answer 1

Answer:

$\frac{114 - 41 \: \sqrt{6}}{30}$

Solution:

$= \frac{3 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48 + \sqrt{18} } }$

The conjugate of √48 + √18 is √48 -√18

$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \times \frac{ \sqrt{48} - \sqrt{18} }{ \sqrt{48} - \sqrt{18} }$

$= \frac{7 \sqrt{3 - 5} - 7 \sqrt{3 \times 18} - 5 \sqrt{48 \times 2} + 5 \sqrt{18 \times 2} }{48 - 18}$

$= \frac{7 \times 12 - 7 \times 3 \sqrt{6 } - 5 \times 4 \sqrt{6} + 5 \times 6 }{30}$

$= \frac{114 - 41 \sqrt{6} }{30}$