Exercise 1535Combinatorics › Binomial coefficientsOlympiadAdded 3 Nov 2026

Approximation via binomial theorem

#approximation#binomial#sqrt

Statement

Use the binomial theorem to approximate $\sqrt{1.02}$ to 4 decimal places.

Hint

$(1+x)^{1/2}=1+\frac{x}{2}-\frac{x^2}{8}+\cdots$ .

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Binomial series. $(1+x)^{1/2}=1+\frac{x}{2}-\frac{x^2}{8}+\frac{x^3}{16}-\cdots$ .

At $x=0.02$ . $\sqrt{1.02}\approx 1+0.01-\frac{0.0004}{8}+\frac{0.000008}{16}\approx1.01-0.00005+0.0000005=1.0099505$ .

Conclusion. $\sqrt{1.02}\approx 1.00995$ .