Question

Determine square root of 0.15? Please tell and explain

Answer 1

≈0.3875.

Explanation:

1) the rule:

f(x₀+Δx)≈f(x₀)+d[f(x₀)]=f(x₀)+f'(x₀)*Δx;

2) f(x)=sqrt(x) and x₀=0.16, then

f(x₀)=0.4; f'(x₀)=1/(2sqrt(x₀))=1/0.8=1.25;

Δx=0.15-0.16=-0.01;

3) finally,

`√(0.15)=√(0.16)-1.25*0.01=0.4-0.0125=0.3875.`