Find the square root of 3-sqrt{5}. | vedclass

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Question

(A) To find the square root of $3-\sqrt{5}$,we write it as $\sqrt{3-\sqrt{5}}$.Multiply and divide by $\sqrt{2}$ inside the square root:$\sqrt{\frac{2

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) To find the square root of $3-\sqrt{5}$,we write it as $\sqrt{3-\sqrt{5}}$.Multiply and divide by $\sqrt{2}$ inside the square root:$\sqrt{\frac{2(3-\sqrt{5})}{2}} = \sqrt{\frac{6-2\sqrt{5}}{2}}$.Now,express the numerator $6-2\sqrt{5}$ as a perfect square:$6-2\sqrt{5} = 5 + 1 - 2\sqrt{5} = (\sqrt{5})^2 + (1)^2 - 2(\sqrt{5})(1) = (\sqrt{5}-1)^2$.Substituting this back,we get:$\sqrt{\frac{(\sqrt{5}-1)^2}{2}} = \frac{\sqrt{5}-1}{\sqrt{2}} = \frac{\sqrt{5}}{\sqrt{2}} - \frac{1}{\sqrt{2}} = \sqrt{\frac{5}{2}} - \frac{1}{\sqrt{2}}$.

Find the square root of $3-\sqrt{5}$.

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