Question

square root of (3+√5) is​

Answer 1

This is the correct answer . Explanation is the answer is attached .

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

Answer 2

$\sqrt{3+\sqrt{5}}=\pm\dfrac{1}{\sqrt{2}}(1+\sqrt{5})$

Step-by-step explanation:

Here, $3+\sqrt{5}$

$=\dfrac{1}{2}(6+2\sqrt{5})$

$=\dfrac{1}{2}(1+2\sqrt{5}+5)$

$=\dfrac{1}{2}[(1)^{2}+2\times 1\times \sqrt{5}+(\sqrt{5})^{2}]$

$=\dfrac{1}{2}(1+\sqrt{5})^{2}$

$=[\dfrac{1}{\sqrt{2}}(1+\sqrt{5})]^{2}$

$\Rightarrow 3+\sqrt{5}=[\dfrac{1}{\sqrt{2}}(1+\sqrt{5})]^{2}$

Now, taking square root to both sides, we have

$\sqrt{3+\sqrt{5}}=\pm \sqrt{[\dfrac{1}{\sqrt{2}}(1+\sqrt{5})]^{2}}$

$\Rightarrow \sqrt{3+\sqrt{5}}=\pm\dfrac{1}{\sqrt{2}}(1+\sqrt{5})$

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