Question

Find the square root of $23$

Answer 1

Find the approximate square root of $23$

First find the nearest perfect square to $23$ .

$25$ is the nearest perfect square around $23$

Now given terms can be written as

$\sqrt{23}=\sqrt{\left(25-2\right)}$

$={25}^{\frac{1}{2}}{\left(1-\frac{2}{25}\right)}^{\frac{1}{2}}$

We know that when when the term is in this form ${(1+x)}^n$ where $x$ is so less than $1$ then it is written as $(1+nx)$

Then according to above condition

$\sqrt{23}=5\left(1-\frac{2}{25}\times \frac{1}{2}\right)$

$$\begin{gathered} =5\left(1-\frac{1}{25}\right) \\ =\left(5-\frac{1}{5}\right) \\ =\left(5-0.20\right) \end{gathered}$$

$\Rightarrow$ $\sqrt{23}=4.80$

Hence the square root of $23$ is approximately equal to $4.80$