Question

Find up to five places of decimals the value of :
$\sqrt{98}$

Answer 1

$⟹{(100-2)}^{\frac{1}{2}}$
$⟹10{(1-0.02)}^{\frac{1}{2}}$
$⟹10\{1-\frac{1}{2}\times 0.02+\frac{\left(\frac{1}{2}\right)(-\frac{1}{2})}{2!}{\left(0.02\right)}^2+\frac{\frac{1}{2}(-\frac{1}{2})(-\frac{3}{2})}{3!}{(-0.02)}^3+...\}$
$⟹10\{1-0.01-\frac{1}{8}\times 0.0004-\frac{1}{16}\times 0.000008\}$
$⟹10\left\{0.989949\right\}$$⟹9.89949$