Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ 2 }{ \sqrt{ \sqrt{ 5 } -1 } }$$

Answer

(sqrt(sqrt(5)-1)*(sqrt(5)+1))/2

Solution


Rationalize the denominator: \(\frac{2}{\sqrt{\sqrt{5}-1}} \cdot \frac{\sqrt{\sqrt{5}-1}}{\sqrt{\sqrt{5}-1}}=\frac{2\sqrt{\sqrt{5}-1}}{\sqrt{5}-1}\).
\[\frac{2\sqrt{\sqrt{5}-1}}{\sqrt{5}-1}\]
Rationalize the denominator: \(\frac{2\sqrt{\sqrt{5}-1}}{\sqrt{5}-1} \cdot \frac{\sqrt{5}+1}{\sqrt{5}+1}=\frac{2\sqrt{\sqrt{5}-1}(\sqrt{5}+1)}{{\sqrt{5}}^{2}-1}\).
\[\frac{2\sqrt{\sqrt{5}-1}(\sqrt{5}+1)}{{\sqrt{5}}^{2}-1}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{2\sqrt{\sqrt{5}-1}(\sqrt{5}+1)}{5-1}\]
Simplify  \(5-1\)  to  \(4\).
\[\frac{2\sqrt{\sqrt{5}-1}(\sqrt{5}+1)}{4}\]
Simplify.
\[\frac{\sqrt{\sqrt{5}-1}(\sqrt{5}+1)}{2}\]

Decimal Form: 1.798907

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