Question

Rationalise the denominator 3√2-2√3/2√6+5

Answer 1

Answer:

27√2 -22√3

Step-by-step explanation:

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{2 \sqrt{6} + 5 } \times \frac{2 \sqrt{6} - 5 }{2 \sqrt{6} - 5} \\ Now \: by \: using \: algebraic \: identities;\\ = > \frac{6 \sqrt{12} - 15 \sqrt{2} - 4 \sqrt{18} + 10 \sqrt{3} }{ {(2 \sqrt{6} )}^{2} - {5}^{2} } \\ = > \frac{12 \sqrt{3} - 15 \sqrt{2} - 12 \sqrt{2} + 10 \sqrt{3} }{24 - 25} \\ = > \frac{22 \sqrt{3} - 27 \sqrt{2} }{ - 1} \\ = > - (22 \sqrt{3 } - 27 \sqrt{2} ) \\ = > - 22 \sqrt{3} + 27 \sqrt{2} \\ Which \: can \: also \: be \: written \: as; \\ 27 \sqrt{2} - 22 \sqrt{3} (required \: answer)$