Chapter 9.1, Problem 68E

To determine

To evaluate: The function $p\left(x\right)=\sqrt{\frac{x-1}{5x}};x=8$ for the given value of x.

Answer to Problem 68E

The required answer is $\frac{\sqrt{7}}{2\sqrt{10}}$ or 0.42.

Explanation of Solution

Given information:

  $p\left(x\right)=\sqrt{\frac{x-1}{5x}};x=8$

Calculation:

  $\begin{array}{l}p\left(x\right)=\sqrt{\frac{x-1}{5x}}\\ p\left(8\right)=\sqrt{\frac{8-1}{5\cdot 8}}\end{array}$

(Replace x by 8)

  $p\left(8\right)=\sqrt{\frac{7}{40}}$

(Simplify)

  $p\left(8\right)=\frac{\sqrt{7}}{\sqrt{40}}$

(Quotient property of square roots)

  $p\left(8\right)=\frac{\sqrt{7}}{\sqrt{4\cdot 10}}$

(Factor using the greatest perfect square factors)

  $p\left(8\right)=\frac{\sqrt{7}}{\sqrt{4}\cdot \sqrt{10}}$

(Product property of square roots)

  $p\left(8\right)=\frac{\sqrt{7}}{2\sqrt{10}}$

Or

  $p\left(8\right)=0.42$