Large Foursquare Roots

In C1, the non-calculator Influenza A virus subtype H5N1 marking module, my pupils sometimes perish stuck solving quadratic equations that are difficult to factorise. This powerfulness live because the leading coefficient is greater than i (see my earlier post) or it may but live because the numbers inward the quadratic are large.  I commonly propose that they persevere amongst factorising, but if they convey to resort to using the quadratic formula in addition to thence they may require to foursquare origin a large foursquare number. Here's roughly uncomplicated ideas for how to create thence - inward this representative I'm finding the foursquare origin of 324, though these methods run every bit good for larger foursquare numbers.

Note that if the quadratic equation can't live factorised inward the commencement house in addition to thence nosotros tin either purpose the formula or consummate the foursquare to solve it, in addition to nosotros volition halt upwards amongst a surd inward our lastly answer.  My adjacent post service is all close didactics surds!