Chapter 8.4, Problem 55PPE

To determine

To find: whether ${\left(3\frac{1}{2}\right)}^2$ is equal to $9\frac{1}{4}$ or not.

Answer to Problem 55PPE

The expression ${\left(3\frac{1}{2}\right)}^2$ is not equal to $9\frac{1}{4}$ .

Explanation of Solution

Given:

The expression is ${\left(3\frac{1}{2}\right)}^2$ .

Calculation:

Simplify the first expression as follows:

  $\begin{array}{l}\Rightarrow {\left(3\frac{1}{2}\right)}^2\\ \Rightarrow {\left(\frac{3\times 2+1}{2}\right)}^2\\ \Rightarrow {\left(\frac{7}{2}\right)}^2\\ \Rightarrow \left(\frac{7\times 7}{2\times 2}\right)\\ \Rightarrow \frac{49}{4}\end{array}$

Simplify the second expression as follows:

  $\begin{array}{l}\Rightarrow 9\frac{1}{4}\\ \Rightarrow \frac{9\times 4+1}{4}\\ \Rightarrow \frac{37}{4}\end{array}$

Thus, the expression ${\left(3\frac{1}{2}\right)}^2$ is not equal to $9\frac{1}{4}$ .