Question

pls help mee ,how to solve this​

Answer 1

Question:

• Rationalise : $\sf\dfrac{1}{8 + 5\sqrt{3}}$

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Solution:

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$:\implies\sf\dfrac{1}{8 + 5\sqrt{3}}\\\\\\:\implies\sf \dfrac{1}{\Big(8 + 5\sqrt{3} \Big)} = \dfrac{1}{\Big(8 + 5 \sqrt{3} \Big)} \times \dfrac{\Big(8 - 5\sqrt{3} \Big)}{\Big( 8 - 5\sqrt{3}\Big)} \\\\\\:\implies\sf \dfrac{\Big(8 - 5 \sqrt{3} \Big)}{\Big(8 \Big)^2 - \Big( 5 \sqrt{3}\Big)^2} \\\\\\:\implies\sf \dfrac{ \Big(8 - 5 \sqrt{3} \Big)}{64 - 75} \\\\\\:\implies\sf \dfrac{\Big(8 - 5\sqrt{3}\Big)}{ \:-11\:} \\\\\\:\implies\sf\dfrac{- \Big(8 - 5\sqrt{3}\Big)}{\ 11 \ }\\\\\\:\implies\sf\dfrac{-8 + 5\sqrt{3}}{\: 11 \:}\\\\\\:\implies{\underline{\boxed{\frak{\pink{\dfrac{5\sqrt{3} - 8}{11}}}}}}$

Answer 2

RATINALISE THE DENOMINATOR

1

________

(8+5√2)

• WE HAVE 1/ (8+5√2)

1= (8+5√2)

SO THE ANSWER IS =(8-5√2)/14

FOR MORE REFER THE ATTACHMENT

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ABHINAV ROCKS10