This prompt can be used as a good discussion prompt. One approach would be to have pupils work in pairs, discussing, before each pair shared their ideas with the class. The task could be used at many levels – for instance with a class who are working on surds, this might be a formative check that they understand sqr(5) + sqr(5) = 2sqr(5). In other contexts it may be used to deepen understanding and appreciation of how irrationals sit on the whole number line.
The results of a discussion in my S1 class are shown below:
@blatherwick_sam suggested the following follow up questions on Twitter:
Could you get an upper and lower bound then of what sqr(5)+sqr(5) could be? What about sqr(3)+sqr(3)? Is sqr(x) + sqr(x) always bigger than sqr(2x)? Why? How about cube roots?oh and this one – sqr(x) + sqr(x) = sqr(10), what is x? and at the top of the board there is in effect a number line… where would 2.5 fall on that number line?