Class 7P from Loretto Junior, Musselburgh apporached this problem using trial and improvement which is a very useful strategy:

Kitty said let's try 600 x 600 = 360000 and that is too big!

Angus said let's try 100 x 100 = 10000 and that is too small.

Ashleigh thought 200 x 200 was 40000 which was a little too small.

Graeme knew that 250 x 250 was 62,500 - close!

Sophie offered 230 x 230 which is 52,900 - getting there.

Gair now tried 240 x 240 and got 57,600.

Tom provided the masterstroke and said our number 56406 should be in the high 230s , so we looked at 236x 237 but the last digit is a 2 because 6x7 = 42.

Finally Caitlin shouted in excitement 'try 237x 238 as the last digit will be a 6'. The answer therefore is 237 x 238.