Finding a square of a 2-digit number in your head

Recently we looked at how to square two-digit numbers ending in 5 in your head.  What about the other square numbers?  Well, there’s a quick way to do that in your head as well.

Let’s look at 372.
First of all round the 37 up or down to the nearest 10.
You added 3 to get 40, so you also need to subtract 3 to get 34 (37-3=34)
Multiply these to numbers together 40×34 = 4 x 34 x 10 = 1360 (4×30=120,  4×4=16, 120 +16 = 136, 136×10=1360)
Finally, add on the square of the number you added and subtracted (here it was 3 and 3×3=9 so add 9) 1360+9=1369.
So 372 = 1369

Here’s another example: 622
Round this down to 60, and then because you subtracted 2, you also have to add 2 so you get 60×64 (6 x 64 x 10). 3 x 60 = 360, 6 x 4 = 24, 360 + 24 = 384, 384 x 10 = 3840
Remember to add the square of the number you rounded down by. 22 = 4 so add 4.
3840 + 4 = 3844
So 622 = 3844

If you’ve enjoyed these tricks then you might enjoy the Secrets of Mental Maths course from The Great Courses. It’s fascinating!

Related post: How to multiply any 2-digit number by 11 (in your head!)

St David’s Day

Every year on 1st March, Wales celebrates its patron saint.  The date marks the day on which St David was said to have died.  But who was St David, why did he become the patron saint of Wales, and how is his day celebrated?

Unlike many saints, whose lives are recorded mainly in legends, St. David was a real, specific person and there are relatively good medieval records of his life.

When he was born is uncertain, with suggested years ranging from 462 to 512 AD depending on the source you read, and various dates given.  However, almost all the documents about St David state that he died on 1st March, although there is debate over the year, with some chronicles recording that he lived to be over 100 years old. Because so many stories said he died on a Tuesday, the year most often suggested is 589, as it is within the range of years in question and 1st March fell on a Tuesday in that year.  While the year may not be certain, the date is something the medieval writers largely agree on, which is why it was taken as the feast day.

St David (or Dewi Sant, as he is known in the Welsh language) was born into an aristocratic family in South West Wales, which meant he received a good education in a local monastery.  The Christian religion played a major part in his upbringing; in fact both his mother (Non) and his teacher (Paulinus) were also venerated as saints.  As an adult, he established a reputation as a preacher and teacher, helping to spread Christianity to pagan tribes in remote areas of Western Britain.  He travelled widely in Wales, South West England and Brittany, with legends also suggesting that he visited both Rome and Jerusalem.  One of the most famous miracles associated with St David is that he was preaching to a large crowd and the ground he was standing on rose up to become a hill, allowing people to see him and hear his message more clearly.

St David is best known for establishing new monasteries in the areas he visited to continue his teaching on a permanent basis, and is said to have founded more than 10 monasteries altogether.  The most important was set up in the area of his birth, in a valley close to the Pembrokeshire coast, and this became his permanent base.  The modern city of St David’s (the smallest city in Britain) and its beautiful cathedral are on the site of that monastery.  As his reputation spread, David was appointed as a bishop, and subsequently became Archbishop of Wales.

David was known for being an extremely spiritual man, who inspired his followers to lead a simple life.  The rules he established for his monks were very strict, even compared to other monastic communities.  Monks had to give up all property (even saying “my book” was considered an offence in this community), spend lots of time in prayer and study, and were forbidden from speaking except for prayer and in emergencies.  They also had to work hard, particularly labouring in the fields around their monastery.  They were not allowed to use animals for power, which meant the men had to pull the ploughs themselves!  Their diet consisted of vegetables and bread, with water and milk to drink.  In terms of his teaching, St David became best known for his “last message” – which was said to have been part of his final sermon before his death.  This encouraged people to “do the little things” – a phrase that became a popular saying in Wales – and to follow his example of a simple life based on prayer, study and hard work.

David was buried in his own cathedral and his tomb soon became a popular place of pilgrimage for Christians who were inspired by his life and teachings.  He was declared a saint in the 11th Century and – unlike many Celtic saints from the same period – is officially recognised by the Roman Catholic church.  The shrine of St David was so important that four pilgrimages to it were considered the equivalent of two to Rome or one to Jerusalem.

St David became established as the national saint of Wales around the 12th Century.  His name was used by writers at that time as a symbol of Welsh identity as the region struggled to resist invasion by the Norman rulers of England.  This status was confirmed in later centuries by him being declared the official patron saint, and his feast day of 1st March has been celebrated as a national day in Wales since the 18th Century.

Although it is not a public holiday – the last attempt to have it named as one was rejected by the UK Parliament a few years ago, despite huge popular support in Wales – the day is marked with many celebrations in Wales and among Welsh people the world over.  Festivities tend to focus on celebrating Welsh identity and culture, rather than specifically being related to the saint himself.  Many villages and towns in Wales have parades, with buildings decorated and people wearing traditional costumes, or Welsh symbols such as the leek or daffodil.  Many schools hold an Eisteddfod, a festival of Welsh-language poetry and music.  To mark the day, the flag of St David (a golden cross on a black background) will often be flown in addition to the national flag of Wales (the more familiar red dragon).

Generally speaking, St David’s Day celebrations are limited to Wales and Welsh communities – the day has not become a more mainstream event as is the case with St Patrick’s Day, for example.  Perhaps the lower-key nature of the day is fitting for a saint who was known for promoting a simple life and who helped to establish a tradition of Christianity and teaching in Wales that continues to this day.

Many thanks to Ian Braisby, Blue Badge Guide, for this post.

Related posts:    St Andrew   St George,    St Patrick