Question

How to find the square root of a number?

I really have a tough time solving Pythagorean Theorem questions because i can't square root a number at the end..

Is there a good and easy way to square root 1-3 digit numbers?

Answer 1

so the best way I know is to break it down into numbers you know the square of, if you can

Answer 2

A calculator.

Answer 3

ie
\[\sqrt(396)=\sqrt(2*198)=\sqrt(4*99)\]

Answer 4

\[=\sqrt(4*3*33)=\sqrt(4*3*3*11)=2*3 * \sqrt(11)=6\sqrt(11)\]

Answer 5

This is also breaking it down into it's prime decomposition

Answer 6

as a side note

Answer 7

Make sense?

Answer 8

So if it were to ask me to find the square root of lets say 150, i would cut 150 in half which is 75? so Square root of 150 is 75 * 2

Answer 9

,,,,prime.....

Answer 10

Or would i go even further?

Answer 11

Until i get to a single or two digit number

Answer 12

Not really.

Answer 13

Until you get only prime numbers.

Answer 14

Are you interested in getting a decimal number, or a simplified expression?

For a decimal number, use a calculator, or google, or wolframalpha.com or any number of websites.

For a simplified expression, factor the quantity under the radical sign into its prime factors: 2,3,5,7,11,13,17,19,23,29,31,37,41,43, etc.

25=5*5
100 = 2*50=2*2*25=2*2*5*5
51 = 3*17
32=2*16=2*2*8=2*2*2*4=2*2*2*2*2

Now to simplify, remember that each pair of identical factors under the radical sign can be moved outside, and replaced by just one:

\[\sqrt{150} = \sqrt{2*75} = \sqrt{2*3*25} = \sqrt{2*3*5*5} = 5\sqrt{2*3}=5\sqrt{6}\]

Answer 15

\[\sqrt{16} = \sqrt{2*2*2*2} = 2*2 = 4\]\[\sqrt{144} = \sqrt{2*72} = \sqrt{2*2*36} = \sqrt{2*2*2*18} \]\[=\sqrt{2*2*2*2*9} =2*2\sqrt{3*3} = 2*2*3 = 12\]

Answer 16

you want to go until you get a prime number

Answer 17

If you want more ammunition for tackling these problems, then you should
1) learn some of the divisibility rules. (This helps you to find factors)
http://www.mathsisfun.com/divisibility-rules.html

2) learn as many of the primes as you can up through 100
http://www.factmonster.com/math/numbers/prime.html

3) Learn as many of the perfect squares as you can
http://www.factmonster.com/ipka/A0875883.html

and of course, know your multiplication table.

Answer 18

I am trying to find the length of the hypotenuse

Answer 19

But they want the square root of 169 which is hard for me to give an answer.

Answer 20

so, that happens to be a special square

Answer 21

one that you have to memorize

Answer 22

169 is a number you might want to memorize.

Answer 23

try calculating the squares of the prime numbers like this 4,9,16,25... Does this come up?

Answer 24

your picture shows 15... do you mean 5 ?

the triplet 3,4,5 is a right triangle
almost as useful, is the 5,12,13 right triangle.

Answer 25

Yes sorry i meant 5

Answer 26

When they tell me to find the square root of 169 i usually start from the tens place and would multiply 11 * (1-12) then 12 * (1-12) and so forth

Answer 27

So i was wondering if there was a method of finding the square root easier.

Answer 28

The easiest way is to be familiar with the squares. you know 1*1, 2*2, and so on (hopefully up to 12*12= 144)

but learn more! 13*13=169

notice that 13 is a prime number, so it would take awhile to figure out 13*13 is the answer...

Answer 29

I don't have a way other than memorization for 169, sorry :/

Answer 30

Are you saying the square root is always a prime number?

Answer 31

if you did not know 144 was 12*12
you could use the divisibility rules to break it into smaller numbers.
for example: it ends in an even number, so 2 divides into. Even better, the last 2 digits (44) is divisible by 4, so the whole number is divisible by 4 to get 4* 36
now take the square root of 4 and of 36 to get 2*6=12 (the square root of 144)
notice that 169 can not be divided by anything (except 13) so we can't do that trick)

Answer 32

no, but 169 happens to be, and the most efficient way when a number is not prime to get a simplified root is to break that number down into its prime decomposition. (the prime numbers multiplied together to get that number)

Answer 33

Ok well i guess it all makes more sense now, thank you both for your quick and great answers, i wish i could give you both medals haha..