Another Maths Question!

[Smowball]

Dont know how to type the correct symbols on here( all help gladly received!).

But what is the easiest way to find the square root of a number?

I know for example that 8 squared is 64, but how say do you find the square root of 196?

[Prudie]

If you mean without a calculator and that the answer is a whole number then trial and error. Try numbers near what you know already eg 10x10 is 100 and 12x12 is 144 so it can't be much more than that. You can also look at the last digit - in this case 6. You can only get squares that end in 6 from numbers with a 4 or 6 at the end. You can only get numbers that end in 1 when starting with a number that ends in 1 or 9 for example.

[Smowball]

Yep I meant without a calculator. Am trying to help son with good methods for maths .

So we knew 144 was 12. And so it couldnt be much higher. It was actually 14 but was hoping there was a proper method

[factor-fiction]

To find the square root of 196 you'd be allowed to use a calculator (square root button) in an exam where calculators are allowed but on a non-calculator paper you'd be expected to use your knowledge of multiplication tables up to 15 x 15.
Ideally a student should be able to reel off the first 15 square numbers from 1x1=1 to 15 x 15 =225. Ideally, I'd suggest students should also know that 20x20= 400 and 100 x 100 =10000

[Maydup]

There's a method detailed here, if you can follow it. I certainly can;t!

http://www.wikihow.com/Calculate-a-Square-Root-by-Hand

[factor-fiction]

Yes, I can work them out in my head to two decimal places by iteration but it has hardly ever come in useful (apart from showing off to the students) and there is absolutely no need for a student to be able to do this at GCSE.

[Prudie]

Well there is if you can put 196 into its prime factors and then put them into 2 equal groups. You start with 2 and keep dividing until it won't go perfectly then try 3, then 5, then 7, then 11 etc (the prime numbers)
196 comes out as 2x2x7x7
split that into two equal groups of 2x7 and 2x7 giving you 2x7 as the square root ie 14

[Smowball]

Thankyou guys, its just interesting that before they so freely allowed calculators into the classroom they must have had to used their.......brains!! lol

[factor-fiction]

We had to use log table books which include square root tables, reciprocals, logs, antilogs, sine cosine , tangent and random number tables, I recall. In my parents' days there were slide rules to help.

[grasscarp]

Have you taught him the easy way for doing eleven times numbers? 11 x 31 is 341, you just add the first and last numbers and put it in the middle. 11 x 22 is 242. It is just a good shortcut if you see number 11 x a 2 digit number

[Smowball]

I must have tired eyes! pls explain again lol

[factor-fiction]

Using prime factors is a good alternative, Prudie.

[grasscarp]

If you are asking me Smow
11 x 12 is 132 (12 is 1 plus 2 which is 3 so put the 3 in the middle)
11 x 42 is 462 (42 is 4 plus 2 which is 6 so put the 6 in the middle)
This is just a short cut which I have found to be useful. I help a friends children with their homework.

[Smowball]

Ahh, ok thankyou! I just like to understand what their teachers are trying to get them to do. Then I know if they are doing it right or not!

[factor-fiction]

And it's even better if they understand why it works, grasscarp
e.g 11x12 is 10 lots of 12 plus 1 lot of 12 which equals 120 +12 =132

[sherrardk]

Hi Smo, they seem to keep changing the way that they 'do' maths. My kids do maths completely differently from the way I did it and the way that himself (ex primary teacher) taught it. God knows how complicated secondary school maths has become.

[Smowball]

Exactly!! My son comes home with ways that make no sense!

[grasscarp]

Factor, I really appreciate your input. However, there are days when even getting them to look at me rather than looking round the room is a challenge. My mother was a maths teacher and I didnt really understand her most of the time!

[factor-fiction]

I know grasscarp, in practice many don't know their tables beyond 4 x 4 even by age 16 and some never do a stroke of work

[grasscarp]

factor. You are so right. I keep on and on at them. You do not know your times tables. I bought them a book with lots of fun exercises on times tables and they did some and have now lost it. I try to say this is going to make the rest of your life easier but they dont believe me.

[Smowball]

I did a test tonight with my son - he had 6 decimal numbers ie 5.6,7.4, to add up. I let him use a calculator - I did it in my head. I was the quickest!