Question

How do you simplify `sqrt87`?

Answer 1

This can be solved easily using a Calculator . We get the answer as `color(green)(approx 9.32738`

But if we are expected to do it without a calculator , here's how it can be done.

`sqrt87 = sqrt(3*29) = sqrt 3 * sqrt 29`

We know that `sqrt 3 approx 1.732`

To find the `color(blue)(sqrt29`, we can use the following formula:

`sqrt(Non-Perfect-Square) approx sqrt(Nearest-Perfect-Square) + (Deviation)/(2*sqrt(Nearest-Perfect-Square))`

The nearest perfect square to 29 is `25`. And the deviation is `29 - 25 = 4`

`sqrt 29 approx sqrt 25 + (4)/(2*sqrt25)`

`approx 5 + (4/10) approx color(blue)(5.4`

Hence we get `sqrt87 approx 1.732 * 5.4 approx color(green)(9.353`