Evaluate: sqrt{3 + sqrt{5}} - sqrt{2 + sqrt{3 | vedclass

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Question

(B) To simplify $\sqrt{3 + \sqrt{5}}$,we multiply and divide by $\sqrt{2}$:$\sqrt{3 + \sqrt{5}} = \sqrt{\frac{6 + 2\sqrt{5}}{2}} = \frac{\sqrt{(\sqrt{

Vedclass · Accepted Answer

$\sqrt{5/2} - \sqrt{3/2}$

Vedclass · Answer

(B) To simplify $\sqrt{3 + \sqrt{5}}$,we multiply and divide by $\sqrt{2}$:$\sqrt{3 + \sqrt{5}} = \sqrt{\frac{6 + 2\sqrt{5}}{2}} = \frac{\sqrt{(\sqrt{5} + 1)^2}}{\sqrt{2}} = \frac{\sqrt{5} + 1}{\sqrt{2}} = \sqrt{\frac{5}{2}} + \sqrt{\frac{1}{2}}$Similarly,for $\sqrt{2 + \sqrt{3}}$,we multiply and divide by $\sqrt{2}$:$\sqrt{2 + \sqrt{3}} = \sqrt{\frac{4 + 2\sqrt{3}}{2}} = \frac{\sqrt{(\sqrt{3} + 1)^2}}{\sqrt{2}} = \frac{\sqrt{3} + 1}{\sqrt{2}} = \sqrt{\frac{3}{2}} + \sqrt{\frac{1}{2}}$Now,subtract the two expressions:$(\sqrt{\frac{5}{2}} + \sqrt{\frac{1}{2}}) - (\sqrt{\frac{3}{2}} + \sqrt{\frac{1}{2}}) = \sqrt{\frac{5}{2}} - \sqrt{\frac{3}{2}}$Thus,the correct option is $B$.

Evaluate: $\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}}$

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