Question

Estimate the square root of 500.

Answer 1

Hint: Firstly, find two perfect squares nearest to 500, from which one square must be smaller than 500 and one must be greater than 500.
Thus, find the value of square roots of the nearest squares.
Finally, find the average value of the above two square roots.
Hence, we get the required estimated value.

Complete step-by-step answer:
We are asked to find the value of the square root of 500.
Now, to do that, we will firstly find the nearest perfect squares to the value 500.
We know that 484 and 529 are perfect squares nearest to 500.
So, $\sqrt{484}=22$ and $\sqrt{529}=23$ .
Thus, the estimated value of $\sqrt{500}$ can be given by the average of the square roots of the two nearest perfect squares.
 $\therefore \sqrt{500}={\displaystyle \frac{22+23}{2}}={\displaystyle \frac{45}{2}}=22.5$
Hence, we get the estimated value of the square root of 500 as 22.5.
 $\therefore \sqrt{500}\approx 22.5$

Note: Here, the estimated value is not the actual answer of the given question.
As, ${\left(22.5\right)}^2=506.25$ , but when we round off the number 506.25 to the nearest 100, we get the answer 500.
Thus, $\sqrt{500}\approx 22.5$ .