Question

Find the approximate value of(0.009)^1/2

Answer 1

We will determine the approximate value of $(0.009)^{\frac{1}{2}}$

 $(0.009)^{\frac{1}{2}}$ =  $(0.008+0.001)^{\frac{1}{2}}$

Taylor's formula states:

$f(a+x)=f(a)+x f'(a)+(\frac{x^{2}}{2})f''(a)+.......$

Let f(a) = $a^{\frac{1}{2}}$

f '(a)= ${\frac{1}{2\sqrt{a}}}$

Let  a =0.008

f(a) = $(0.008)^{\frac{1}{2}}$

= 0.089

f '(a) = $\frac{1}{2\sqrt{0.008}}$

= 5.59

Let x = 0.001

f(0.009) is approximately equal to

= f(0.008) + 0.001 $\times$ f'(0.008)

= 0.089 + 0.001(5.59)

= 0.094

Hence, the approximate value is 0.094