Question

Rationalise the denominator of 4/ 2+√3+√7

Answer 1

Answer:

Step-by-step explanation:

your answer

Answer 2

$\huge \matfrak \red{answer}$

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$\huge \sf \underline{Question}$

Rationalise the denominator of 4/ 2+√3+√7

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Step by step explanation:

$\sf{⟹ \: \frac{4}{2 + \sqrt{3} + \sqrt{7} }}$

now multiply the Numerator and denominator we get,

$\sf \red{⟹ \: \frac{4(2 + \sqrt{3} + \sqrt{7} }{(2 + \sqrt{3}) + \sqrt{7}(2 + \sqrt{3}) - \sqrt{3} }}$

$\sf \blue{⟹ \: = \frac{4(2 + \sqrt{3} - \sqrt{7}) }{(2 + \sqrt{3} {}^{2} - ( \sqrt{7) {}^{2} } }}$

$\sf \pink{⟹ \: = \frac{4 + (2 + \sqrt{3} - \sqrt{7}) }{ {2}^{2} + 2 \times 2 \times \sqrt{3} + ( \sqrt{3}) {}^{2} - 7} }$

$\sf \orange{⟹ \: = \frac{4(2 + \sqrt{3} - \sqrt{7} }{4 + 4 \sqrt{3} + 3 - 7} }$

$\sf \green{⟹ \: = \frac{4(2 + \sqrt{3} - \sqrt{7} }{4 \sqrt{3}} }$

$\sf \ red{⟹ \: = \frac{2 + \sqrt{3} - \sqrt{7} }{ \sqrt{3}} }$

$\sf \blue{⟹ \: = \frac{2 + \sqrt{3} - \sqrt{7} }{3}}$

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Now rationalize the denominator we get,

$\sf \pink{⟹ \: = \frac{(2 + \sqrt{3} - \sqrt{7} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3}} }$

$\sf \green{⟹ \: = \frac{(2 \sqrt{3 + 3 - \sqrt{21)} } }{3}}$

$\sf \orange{⟹ \: = \frac{4}{2 + \sqrt{3} + \sqrt{7} = </p><p> \frac{(2 \sqrt{3 + 3 - \sqrt{21} } }{3} } }$

I hope it's help uh