Use linear approximation, i.e. the tangent line, to approximate $\displaystyle \sqrt{{{25.4}}}$ as follows:
Let $\displaystyle {f{{\left({x}\right)}}}=\sqrt{{x}}$. Find the equation of the tangent line to $\displaystyle {f{{\left({x}\right)}}}$ at $\displaystyle {x}={25}$

$\displaystyle {L}{\left({x}\right)}$ = Preview Question 6 Part 1 of 2  

Using this, we find our approximation for $\displaystyle \sqrt{{{25.4}}}$ is
Preview Question 6 Part 2 of 2  
NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer.