Question

How to rationalize 1/2+root 5

Answer 1

Step-by-step explanation:

1/2+√5

1/2+√5×2-√5/2-√5

2-√5/(2+√5)(2-√5)

2-√5/4-5

2-√5/-1

-2+√5/1

-2√5

Answer 2

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How to rationalize $\frac{1}{2\:+\:\sqrt{5}}$ ?

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$+\sqrt{5}$ - 2

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=> $\frac{1}{2\:+\:\sqrt{5}}$

=> $\frac{1}{2\:+\:\sqrt{5}} × \frac{2\:-\:\sqrt{5}}{2\:-\:\sqrt{5}}$

0_0 --> We used actually (a - b)(a + b) =($a^{2} - b^{2}$)^_^ 

=> $\frac{2\: - \:\sqrt{5}}{2^{2} - \sqrt{5}^{2}}$

=> $\frac{2\: - \:\sqrt{5}}{4\: - 5}$

=> $\frac{2\: - \:\sqrt{5}}{-1}$

=> $\frac{2\:-\:\sqrt{5}}{-1} × \frac{-1}{-1}$

=> $\frac{+\sqrt{5}\:-\:2}{+1}$ (Ans)

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