Question

rationalise the denominator of the following:-
i) 5√7/√3
ii) 1/√5+√2
​

Answer 1

Answer:

i)

$\frac{5 \sqrt{21} }{3}$

ii)

$\frac{5 - \sqrt{2} }{23}$

Step-by-step explanation:

i)

$\frac{5 \sqrt{7} }{ \sqrt{3} } = \frac{5 \sqrt{7} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ = \frac{5 \sqrt{21} }{3}$

ii)

$\frac{1}{5 + \sqrt{2} } = \frac{1}{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} } \\ = \frac{5 - \sqrt{2} }{ {(5)}^{2} - {( \sqrt{2}) }^{2} } \\ = \frac{5 - \sqrt{2} }{25 - 2} \\ = \frac{5 - \sqrt{2} }{23}$

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