Question

Rationalize the deominator
a.2/(_/3-1
b.7/(_/12-_/5)
c.1/(8+3_/5)​

Answer 1

(I)

$\frac{2}{ \sqrt{3} - 1 } = \frac{2}{ \sqrt{3} - 1 } \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 } \\ = \frac{2( \sqrt{3 } + 1) }{ {( \sqrt{3}) }^{2} - {(1)}^{2} } = \frac{2( \sqrt{3} - 1 }{3 - 1} = \\ \frac{2( \sqrt{3} - 1) }{2} = \frac{ \sqrt{3} - 1 }{1}$

(ii)

$\frac{7}{ \sqrt{12} - \sqrt{5} } = \frac{7}{ \sqrt{12} - \sqrt{5} } \times \frac{ \sqrt{12} + \sqrt{5} }{ \sqrt{12} + \sqrt{5} } \\ = \frac{7( \sqrt{12} + \sqrt{5} ) }{ { \sqrt{(12)} }^{2} - { \sqrt{(5)} }^{2} } = \frac{7( \sqrt{12} + \sqrt{5} )}{7} = \frac{ \sqrt{12} + \sqrt{5} }{1}$

(iii)$\frac{1}{8 + \sqrt[3]{5} } = \frac{1}{8 + \sqrt[3]{5} } \times \frac{8 - \sqrt[3]{5} }{8 - \sqrt[3]{5} } \\ = \frac{8 - \sqrt[3]{5} }{ {(8)}^{2} - {( \sqrt[3]{5}) }^{2} } = \frac{8 - \sqrt[3]{5} }{64 - (9 \times 5)} \\ = \frac{8 - \sqrt[3]{5} }{24}$

I think it's correct

please mark brainliest