Chapter 12, Problem 12STP

To determine

To calculate:To estimate $\sqrt{125}$ to the nearest integer without using calculator

Answer to Problem 12STP

  $\sqrt{125}=11.18$

Explanation of Solution

Given information:Expression is $\sqrt{125}$

Formula Used:

Pythagoras theorem states that in a right triangle ABC, right angled at B we have

  $A{C}^2=A{B}^2+B{C}^2$

Calculation:

Expression is given as follow:

  $\sqrt{125}$

On simplifying using long division method

  $1\begin{array}{c}\hfill 11.18\\ \hfill \overline{)\begin{array}{l}125\\ 1\\ --\\ 21\overline{)\begin{array}{l}025\\ 021\\ ---\\ 221\overline{)\begin{array}{l}00400\\ 00221\\ -----\\ 2228\overline{)\begin{array}{l}0017900\\ 0017824\\ ------\\ 0000076\end{array}}\end{array}}\end{array}}\end{array}}\end{array}$

Thus, $\sqrt{125}=11.18$

Conclusion:

Hence, $\sqrt{125}=11.18$