Question

What is the approximate value of this square root?

Answer 1

Answer:

12.1

Step-by-step explanation:

To approximate this value, we simply need to know some perfect squares.  We know that the value 144 is the perfect square of 12.  And we know the value 169 is the perfect square of 13.

Note, that our value, 146 is far closer to 144 than to 169, so we know that we will be close to 12 as our approximation.

The distance from 144 to 146 is 2, while the distance from 169 to 146 is 23.

A rough fractional approximation can be found with 2/23 approximately 0.08.

For the solution then, our approximation of sqrt(146) ~= 12.08 ~= 12.1

Cheers.