Large Foursquare Roots

In C1, the non-calculator H5N1 degree module, my pupils sometimes conk stuck solving quadratic equations that are difficult to factorise. This mightiness live on because the leading coefficient is greater than i (see my earlier post) or it may only live on because the numbers inwards the quadratic are large.  I usually propose that they persevere amongst factorising, but if they accept to resort to using the quadratic formula together with thence they may need to foursquare origin a large foursquare number. Here's only about elementary ideas for how to produce thence - inwards this example I'm finding the foursquare origin of 324, though these methods travel as good for larger foursquare numbers.

Note that if the quadratic equation can't live on factorised inwards the outset house together with thence nosotros tin either role the formula or consummate the foursquare to solve it, together with nosotros volition destination upwardly amongst a surd inwards our finally answer.  My side past times side post service is all most didactics surds!

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