Chapter 9, Problem 25CR

To determine

Towrite:The given sentence using $>$ , $<$ or $=$

Answer to Problem 25CR

  $5\frac{1}{2}<\sqrt{48}$

Explanation of Solution

Given information:

  $5\frac{1}{2}\_\_\sqrt{48}$

Concept Used:

When two quantities are not equal, the comparison between them is often presented by certain symbols, this comparison is known as inequality and the symbols used for such comparison are known as inequality symbols.

There are four inequality symbols, $>$ , $<$ , $\ge$ , $\le$ namely “greater than”, “less than”, “greater than or equal to” and “less than or equal to” respectively.

If the two numbers are equal, they are represented by $=$

Calculation:

  $\begin{array}{l}5\frac{1}{2}\\ =5+\frac{1}{2}\\ =\frac{5\left(2\right)+1}{2}\\ =\frac{10+1}{2}\\ =\frac{11}{2}\\ =5.5\end{array}$

  $\begin{array}{l}\sqrt{48}\\ =\sqrt{6·7}\\ =6.9282\end{array}$

As $5.5<6.9282$

Therefore,

  $5\frac{1}{2}<\sqrt{48}$