Chapter ISG, Problem 7.4.8P

To determine

To justify the given statement.

Explanation of Solution

Given information:

Formula used: Number system theory.

And,

Area of rectangle= $l\times b$

Where $l$ is length and $b$ is breadth.

Let’s take an example:

  $\begin{array}{l}x=\sqrt{65}\\ y=\sqrt{260}\end{array}$

Area of rectangle= $l\times b$

Substituting the values,

  $A=\sqrt{65}\times \sqrt{260}$

  $\sqrt{260}$ canbe written as $\sqrt{65\times 4}$

  $A=\sqrt{65}\times \sqrt{65\times 4}$

On solving,

  $A=\sqrt{65}\times \sqrt{65}\times \sqrt{4}$

So,

  $A=65\times \sqrt{4}$

  $\sqrt{4}$ is 2

  $A=65\times 2$

So,

  $A=130$

Which is a rational number and within 100 and 200.