Question

describe a method of approximating the square root of 32

Answer 1

A method of approximating would be say 5x5=25 and 6x6=36 so you know that 32 is between 5 and 6

Answer 2

First, find a square root hat is equal to a whole number which is slightly less than the one we have already. For example, $\sqrt{25} = 5$. $\sqrt{25}$ is a good choice because 25 is just a bit smaller than 32.

Now, we are going to pick a square root which is equal to a whole number where the values under the radical sign is just slightly larger than 32. For example, $\sqrt{36}$ is a good example, because it equals 6, and 36 is just slightly larger than 32.

Now, we have said that $\sqrt{25}$ (which equals 5) is just less than $\sqrt{32}$ and that $\sqrt{36}$ (which equals 6) is just slightly larger than $\sqrt{32}$. Represented mathematically, this would appear as:

$\sqrt{25} < \sqrt{32} < \sqrt{36}$

Since we have found values for $\sqrt{25}$ and $\sqrt{36}$, we can "plug" them into our expression:

$5 < \sqrt{32} < 6$

We can see that $\sqrt{32}$ is a number between 5 and 6. It appears to be just a little over the average of 25 and 36, so we can approximate our value just a little over the average of 5 and 6. The average of 5 and 6 is about 5.5, so we will approximate $\sqrt{32}$ to be 5.65.