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Estimating the Square Root

If √ 2 =1.4...

Question

If $\sqrt{2} = 1.414$ , then find the value of $\frac{1}{1 - \sqrt{2}}$

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Solution

$\frac{1}{1 - \sqrt{2}} = \frac{\sqrt{2} + 1}{1 - 2} = - (1 + \sqrt{2}) = - 2.414$

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