Question

How do you find the square root of 18? Needs to be in decimal form and we cannot use calculators

Answer 1

Answer: $\sqrt{18}\text{ = 4.25}$

Explanation:

Given:

$\sqrt{18}$

To find:

The root of 18 without using a calculator

There is a formula that gives an approximation of a square root without a calculator. This is given as:

$\begin{gathered} \sqrt{N}\text{ = }\frac{N\text{ + M}}{2\sqrt{M}} \\ where\text{ N = is the number we want to find its root} \\ M\text{ = is a perfect square close the number we are to find} \\ That\text{ is a number we can find its root } \end{gathered}$$\begin{gathered} \text{N = 18} \\ M\text{ = 16 is the closest number to 18 we can find its root} \\ \\ substitute\text{ the values into the formula:} \\ \sqrt{18}\text{ = }\frac{18\text{ + 16}}{2\times\sqrt{16}} \\ \\ \sqrt{18}\text{ = }\frac{34}{2(4)} \end{gathered}$$\begin{gathered} \sqrt{18}\text{ = }\frac{34}{8} \\ \\ \sqrt{18}\text{ = 4.25} \end{gathered}$