Estimating Square Roots of non-perfect Square Numbers
We have learned how to find square roots of perfect squares. However, when numbers are not perfect squares, we cannot find their exact square roots. In such cases, we need to estimate the square root.
Let us estimate the value of √520 to the nearest whole number.
520 lies between two perfect square numbers
∴ 484 < 520 < 529
22² < 520 < 23² i.e., 22 < √520 < 23
Since 520 is closer to 529 than to 484, the approximate value of √520 is 23.
This method shows how we can estimate square roots by:
(1) Finding the perfect squares the number lies between
(2) Taking the square roots of those perfect squares
(3) Comparing the distance to each perfect square to determine which whole number is closer