sqrt{3 + sqrt{5}} - sqrt{2 + sqrt{3}} = | vedclass

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Question

(B) To simplify $\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}}$,we multiply and divide by $\sqrt{2}$ inside the square roots:$\sqrt{3 + \sqrt{5}} - \sqrt{

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) To simplify $\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}}$,we multiply and divide by $\sqrt{2}$ inside the square roots:$\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}} = \sqrt{\frac{6 + 2\sqrt{5}}{2}} - \sqrt{\frac{4 + 2\sqrt{3}}{2}}$$= \frac{\sqrt{(\sqrt{5})^2 + 1^2 + 2\sqrt{5}}}{\sqrt{2}} - \frac{\sqrt{(\sqrt{3})^2 + 1^2 + 2\sqrt{3}}}{\sqrt{2}}$$= \frac{\sqrt{(\sqrt{5} + 1)^2}}{\sqrt{2}} - \frac{\sqrt{(\sqrt{3} + 1)^2}}{\sqrt{2}}$$= \frac{\sqrt{5} + 1}{\sqrt{2}} - \frac{\sqrt{3} + 1}{\sqrt{2}}$$= \frac{\sqrt{5} + 1 - \sqrt{3} - 1}{\sqrt{2}}$$= \frac{\sqrt{5} - \sqrt{3}}{\sqrt{2}}$$= \sqrt{\frac{5}{2}} - \sqrt{\frac{3}{2}}$

$\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}} = $

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