Question

Estimate the value $\sqrt{300}$ to the nearest whole number.

Answer 1

Let us estimate the value of 300 to the nearest whole number.
300 lies between two perfect square numbers 100 and 400
$\therefore 100<300<400$
${10}^2<300<{20}^2$
i,.e. $10<\sqrt{300}<20$
But still we are not very close to the square number. We know that
${17}^2=289,{18}^2=324$
Therefore, 289 < 300 < 324

As 289 is more closer to 300 than 324.
The approximate value of $\sqrt{300}$ is 17.