Estimating a square root

Estimating a square root

IB Year 5 | Grade 11
5 marks

Expand \(\sqrt{1+x}\) up to the term in \(x^3\). Use your expansion to estimate \(\sqrt{1.08}\), giving the value of the truncated expression exactly as a decimal.[5]

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Answer:\(1+\frac12x-\frac18x^2+\frac1{16}x^3+\cdots;\ 1.039232\)

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