What’s the relationship between division and square roots in students’ minds? Why did the kid write 15 / 15.

[Note: no idea how to categorize this in CCSS. Also, thanks to Timon for the submission.]

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- Post author By mpershan
- Post date June 27, 2013
- 5 Comments on Division and Square Roots

## 5 replies on “Division and Square Roots”

Is this the logic? 15^2 = 15*15 so sqrt(15) = 15/15. But why doesn’t the answer = 1?

This student seems to understand the concept of a square root, as evidenced by the approx. of 3.9 being a little less than 4, which would’ve been sqrt(16). Seems as if he’s trying to show the opposite of repeated mult., which we’ve seen as a go to for students when they’re considering exponents. Maybe he’s having difficulty with going from the abstraction of the concept in his head to the concrete numerical expression on paper?

Approximating square roots is an 8th Grade standard — 8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g. pi squared).

It could be that the student got caught in the long division vs square root debacle.

I agree with Ines. However the answer probably doesn’t equal 1 because the student probably used a calculator and put in sqrt (15) instead of 15/15.