The square root of a number?

One way is to begin "sensible guessing"...

i.e. 820

We know 30 x 30 = 900 so it has to be less than 30.

We know 20 x 20 = 400 so it is more than 20.

And use this process until you get near to your answer.

25 x 25 = 625

28 x 28 = 784 (36 away from 820)

29 x 29 = 841 (21 away from 820)

So it's nearer to 29 than it is to 28...

Hope that helps.

In order to do this, you have to learn a square root algorithm. Get out a piece of paper and a pencil. I hope that I can explain it well enough just using words.

First, write down the decimal 7.00000000 and mark off pairs of digits starting from the decimal point. This gives you 7.00'00'00'00'...

To start, guess at the square root of 7. The nearest integer(without going over) is 2. Now set the thing up like a long division.

2 divides into 7 2 times. 2 x 2 = 4. Subtract that from 7 which leaves 3 and bring down the next two digits.

Now comes the part that's different from division. The answer showing so far is 2. Double that and use the 4 as the first digit of a new divisor. Whatever goes in the one's place must also go up in the answer. In other words, the question is: forty something goes into 300 how many times?. The answer is 6. Forty-six times six = 276.

Subtract that from 300 leaving 24.

Bring down the next two zeros. Double what's in the answer (double 26). Use 52 as the first two digits in a new divisor and the question becomes five hundred and twenty something divides into twenty-four hundred how many times? The answer is 4. 4 times 524 = 2096.

Subtract from 2400. Bring down two more zeros. Double the answer and leave an empty digit and so on and so forth.

You can keep going forever. So now, you know you are smarter than a calculator!

Once you see how this goes, it's not that hard. If you want a hard one, try the algorithm for finding a cube root (I don't know it).

Hope that you can follow this.

JUST PRIME FACTORIZE THE NUMBER.

FOR EXAMPLE-

IF YOU WANT TO FIND THE SQUARE ROOT OF 900.

THEN PRIME FACTORIZE 900 i.e.

FIND ALL THE FACTORS OF 900 WHICH ARE PRIME.

SO, WE CAN WRITE 900 AS

900 = 2 X 3 X 5 X 2 X 3 X 5

= 2^2 (SQUARE OF 2 i.e 4) X 3^2 X 5^2

= (2 X 3 X 5)^2

= 30^2

900 = 30 X 30

SQUARE ROOT OF 900 = 30

THERE MANY OTHER WAYS-

http://math.arizona.edu/~kerl/doc/square-root.html

http://www.homeschoolmath.net/teaching/square-root...

http://www.rism.com/Trig/square.htm

THESE SITES WILL REALLY HELP YOU A LOT.

Square Root Of 820

In the set of real numbers, the square root of a negative number does not exist. However in the set of complex numbers a special " number " is defined such as ( i )^2 = -1 Now the square root of a negative number is possible. For example since ( 3i )^2 = 9 i^2 and i^2 = - 1 we get ( 3i )^2 = -9 .Then the square root of -9 is 3i.

This Site Might Help You.

RE:

The square root of a number?

I want to work out the square root of a number without using a calculator but I have forgotten how to do it. Yes I know how to do it on a calulator

Scroll down to find out

A bit more

Keep going

Keep going

Nearly there

You find out all the primes and then you take one of every two of the same primes

e.g

256=2*2*2*2*2*2*2*2

There are eight 2s so you only take four 2s.

Then you times them together.

2*2*2*2=16

example 2

144=2*2*2*2*3*3

There are four 2's and two 3's

You take two 2's and one 3's

2*2*3= 12

Example 1= Square root of 256=16

Example 2= Square root of 144=12

Hope it helps.

1) By division method

2) By approximate method.

Division method is difficult to explain here.

approximate method e.g. √1521 you must know the method to find the square of numbers ending with 5.

you know 30² = 900, 40² = 1600

so square root of 1521 lies between 30 and 40

now 35² = 1225

so square root of 1521 lies between 35 and 40

number 1521 is having 1 in the unit place. so the square root must have 1 or 9 in the unit place.

but our number is between 35 & 40

therefor squaare root must be 39

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The square root of -8 is 8i. They're called imaginary numbers, you'll probably learn about them in Algebra II

square root is a number multiplied by itself