Large Square Roots

In C1, the non-calculator A level module, my pupils sometimes get stuck solving quadratic equations that are hard to factorise. This might be because the leading coefficient is greater than one (see my earlier post) or it may just be because the numbers in the quadratic are large.  I normally suggest that they persevere with factorising, but if they have to resort to using the quadratic formula then they may need to square root a large square number. Here's some simple ideas for how to do so - in this example I'm finding the square root of 324, though these methods work equally well for larger square numbers.

Note that if the quadratic equation can't be factorised in the first place then we can either use the formula or complete the square to solve it, and we will end up with a surd in our final answer.  My next post is all about teaching surds!