Question

2) Rationalise the denominator 8/ 3√2+ √​5

Answer 1

Answer:

24√2-8√5/13

Step-by-step explanation:

$\green{Rationalizing}$

$\frac{8}{3 \sqrt{2} + \sqrt{5} }$

$\frac{8}{3 \sqrt{2} + \sqrt{5} } \times \frac{3 \sqrt{2} - \sqrt{5} }{3 \sqrt{2} - \sqrt{5} }$

$\frac{24 \sqrt{2} - 8 \sqrt{5} }{(3 \sqrt{2} ) {}^{2} - ( \sqrt{5}) {}^{2} }$

$\frac{24 \sqrt{2} - 8 \sqrt{5} }{18 - 5}$

$\frac{24 \sqrt{2} - 8 \sqrt{5} }{13}$

hence factorised

identity used:

$\large{(a+b)(a-b)=a^2-b^2}$