Question

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

Answer 1

Answer:
`√(18)\text{ = 4.25}`

Step-by-step explanation:

Given:

`√(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} √(N)\text{ = }\frac{N\text{ + M}}{2√(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:} \\ √(18)\text{ = }\frac{18\text{ + 16}}{2*√(16)} \\ \\ √(18)\text{ = }(34)/(2(4)) \end{gathered}`
`\begin{gathered} √(18)\text{ = }(34)/(8) \\ \\ √(18)\text{ = 4.25} \end{gathered}`