Louise of Headington Junior School gives the answer of 237 and 238.
"I worked this out by finding the square root of 56,406 and then
wrote down the whole number (237) and rounded it up to 238".
Class 7P from Loretto Junior, Musselburgh apporached this
problem using trial and improvement which is a very useful
Kitty said let's try 600 x 600 = 360000 and that is too
Angus said let's try 100 x 100 = 10000 and that is too
Ashleigh thought 200 x 200 was 40000 which was a little too
Graeme knew that 250 x 250 was 62,500 - close!
Sophie offered 230 x 230 which is 52,900 - getting
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.