1. No number has the same square root as its cube root.
True or false?
N1.2 Core Plenary
A million small cubes can be put together to make a large cube with no cubes left over.
A thousand small square tiles can be put together to make a larger square with no small squares left over.
No number has the same square root as its cube root.
The square of any number is always larger than the number itself.
You can disprove a rule by finding one case where it does not work.
You cannot prove a rule just by finding a large number of cases where it works.
Preamble
A collection of ‘true or false?’ number questions, based on the section content, which should involve pupils justifying their answers.
There is some scope for pupils to construct their own true or false questions.
Possible content
Disproving a rule using a counter-example.
Resources
None.
Solution/Notes
True – the cube root of is a whole number (100 × 100 × 100 = ).
False – the square root of 1000 is not a whole number.
False – the square root of 1 and the cube root of 1 are both equal to 1.
False – squaring a number between 0 and 1 will give a smaller answer.
For example 0.5 × 0.5 = 0.25
Original Material © Cambridge University Press 2009
Original Material © Cambridge University Press 2009