Question

rationalize it

FULL SOLUTIONS WILL GET BRAINLISTED ​

Answer 1

Answer:

I solved it in my computer. Check attachment ❄️

Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• $\sf \dfrac{\sqrt{5} \: - \: 2}{\sqrt{5} \: + \: 2}$

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Rationalise the given fraction

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• $\sf \dfrac{\sqrt{5} \: - \: 2}{\sqrt{5} \: + \: 2}$

We know that,

• Rationalising factor of denominator i.e

• $\sf \sqrt{5} \: + \: 2 \: is \: \sqrt{5} \: - \: 2$

Multiplying numerator and denominator with $\sf \sqrt{5} \: - \: 2$ ,

• $\sf \dfrac{\sqrt{5} \: - \: 2}{\sqrt{5} \: + \: 2} \: * \: \dfrac{\sqrt{5} \: - \: 2}{\sqrt{5} \: - \: 2}$

• $\sf \dfrac{(\sqrt{5} \: - \: 2)^2}{(\sqrt{5} \: + \: 2) \: * \: (\sqrt{5} \: - \: 2)}$

• $\sf \dfrac{(\sqrt{5})^2 \: + 2^2 \: - \: 2 \: * \: \sqrt{5} \: * \: 2}{(\sqrt{5})^2 \: - \: 2^2}$

• $\sf \dfrac{5 \: + \: 4 \: - 4\sqrt{5}}{5 - 4}$

• $\sf \dfrac{9 \: - \: 4\sqrt{5}}{1}$

• $\sf 9 \: - \: 4\sqrt{5}$

Therefore,

• $\sf \dfrac{\sqrt{5} \: - \: 2}{\sqrt{5} \: + \: 2} \: = \: 9 \: - \: 4\sqrt{5}$