Chapter 12.3B, Problem 11GCE

To determine

To find:

Thevalue of the given order.

Answer to Problem 11GCE

  $3.875$

Explanation of Solution

Given:

The value is

  $\sqrt{15}$

Concept used:

Formula:

  $n^2-1$

Calculation:

$15=4^2-1$ Is of the form $n^2-1$

Fraction expression

  $\sqrt{15}\approx \left[3;1,6,1\right]$

  $\begin{array}{l}=3+\frac{1}{1+\frac{1}{6+\frac{1}{1}}}\\ =3+\frac{1}{1+\frac{1}{7}}\\ =3+\frac{7}{8}\\ =\frac{31}{8}\\ =3.875\end{array}$