Question

5-√3/√3+4 rationalise the denominator​

Answer 1

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Answer 2

ANSWER:

To rationalize:

• (5 - √3)/(√3 + 4)

Solution:

$\text{We are given that,}\\\\:\longrightarrow\dfrac{5-\sqrt3}{\sqrt3+4}\\\\\text{Multiplying and Dividing by \sqrt3-4 ,}\\\\:\implies\dfrac{5-\sqrt3}{\sqrt3+4}\times\dfrac{\sqrt3-4}{\sqrt3-4}\\\\:\implies\dfrac{(5-\sqrt3)(\sqrt3-4)}{(\sqrt3+4)(\sqrt3-4)}\\\\\text{We know that,}$

$:\hookrightarrow(a-b)(a+b)=a^2-b^2\\\\\text{So,}\\\\:\implies\dfrac{(5-\sqrt3)(\sqrt3-4)}{(\sqrt3+4)(\sqrt3-4)}\\\\:\implies\dfrac{5\sqrt3-20-3+4\sqrt3}{(\sqrt3)^2-4^2}\\\\:\implies\dfrac{9\sqrt3-23}{3-16}\\\\:\implies\dfrac{9\sqrt3-23}{-13}\\\\:\implies\dfrac{-(9\sqrt3-23)}{13}\\\\\bf{:\implies\dfrac{23-9\sqrt3}{13}}$

Formula Used:

$:\hookrightarrow(a-b)(a+b)=a^2-b^2$