Chapter 10: Infinite Sequences and Series - Section 10.9 - Convergence of Taylor Series - Exercises 10.9 - Page 625: 40

$\space |\space Error| \lt 1.25 \times 10^{-5}$

Recall the Binomial series for $\sqrt{1+x}=1+\dfrac{x}{2}-\dfrac{x^2}{8}+\dfrac{x^3}{16}-.....$ By the Alternating Series Estimation Theorem, the error can be computed as: $|Error| \lt |\dfrac{-x^2}{8}| $ $\implies \space |Error| \lt \dfrac{(0.01)^2}{8} $ Thus, $\space \implies |\space Error| \lt 1.25 \times 10^{-5}$