Question

Find the approximate value of $\sqrt{3}$ (upto 2 decimal point)

Answer 1

We know that, largest perfect square less than $3$ is 1 and smallest perfect square greater than $3$ is 4.
$\Rightarrow 1<3<4\Rightarrow \sqrt{1}<\sqrt{3}<\sqrt{4}\Rightarrow 1<\sqrt{3}<2$

Now, largest perfect square less than $300$ is $289$ and smallest perfect square greater than $300$ is $324.$
$\Rightarrow 289<300<324\Rightarrow 2.89<3.00<3.24\Rightarrow \sqrt{2.89}<\sqrt{3.00}<\sqrt{3.24}\Rightarrow 1.7<\sqrt{3}<1.8$

Now, largest perfect square less than $30,000$ is $29,929$ and smallest perfect square greater than $30,000$ is $30,276.$
$\Rightarrow 29,929<30,000<30,276\Rightarrow 2.9929<3.0000<3.0276\Rightarrow \sqrt{2.9929}<\sqrt{3.0000}<\sqrt{3.0276}\Rightarrow 1.73<\sqrt{3}<1.74$

$\therefore$ Approximate value of $\sqrt{3}$ is $1.73$