I’d start with “Can you apply the same procedure to simplify the square root of 12?” and see what I got from there. Do they think that the square root of 12 is equal to 12? Do they think that this procedure only applies when there’s a + or – sign? Is there some other reason for this process? Then I’ll know enough to help them further.

I also wonder about factoring out the square root of 3 from both terms. Most people (me included!) tend to have the habit of simplifying each square root separately first. Would it be good to do some factoring here to connect it with some of the other patterns students have learned?

Ask them to estimate what the square root of 12 is. Hopefully they will say between 3 and 4. Then ask them to estimate what the square root of 27 is. Have them come up with an estimated solution and then have them estimate what their solution will produce.

## 2 replies on “Over-rationalizing”

I’d start with “Can you apply the same procedure to simplify the square root of 12?” and see what I got from there. Do they think that the square root of 12 is equal to 12? Do they think that this procedure only applies when there’s a + or – sign? Is there some other reason for this process? Then I’ll know enough to help them further.

I also wonder about factoring out the square root of 3 from both terms. Most people (me included!) tend to have the habit of simplifying each square root separately first. Would it be good to do some factoring here to connect it with some of the other patterns students have learned?

Ask them to estimate what the square root of 12 is. Hopefully they will say between 3 and 4. Then ask them to estimate what the square root of 27 is. Have them come up with an estimated solution and then have them estimate what their solution will produce.