If \sqrt{2} = 1.4142 then \sqrt{\frac{\sqrt{2}

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Irrational Number

Rationalisation

Question

\sqrt{2} = 1.4142

then

\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} =

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\frac{\sqrt{\frac{(\sqrt{2} - 1)}{(\sqrt{2} + 1)} \times \frac{(\sqrt{2} - 1)}{(\sqrt{2} - 1)}}}{\sqrt{\frac{(\sqrt{2} - 1)^{2}}{2 - 1}}} = \sqrt{(\sqrt{2} - 1)^{2}}

= \sqrt{2} - 1, = 1.4.42 - 1

= 0.4142