How to find the √ without using a calculator?

Question

How to find. Without a calculator, show steps, and explain briefly.

btw. Im not going to use like 23*23 method its too long. I need to find an easier way.

√529=
&
√1024

NOTES: Theres like a way using √9*49= 3*7=21 but how to apply it here.

Answer 1

All right, 529 is between 400 and 900, which sqrts are 20 , 30

Between 20 and 30 find a # that if squared LSD(least SIG Digit)

IS 9 , WELL U GOT IT , 23 OR 27 PICK ONE.

You can do it in your head, it is very easy.

let's do 1024, is between 900 and 1600, or 30 and 40, so it is

30 or 31,32,33,34,35,36,37,38,39 and 40

you want to pick a number that when u multiply by itself the LSD to be 4, only 2choices 32 or 38.

32x32= 1024 bingo on first strike. Try it U will like it.

Good Luck and Best Regards.

Answer 2

The object is to find the highest squared number that factors into the original number and pull that out. It's easier said then done without a calculator however, so the easiest thing to do is start by trying divide the number evenly by the smallest whole number.

In the case of sq rt of 529, 2 does not divide evenly, so you then go on to 3, 4, 5, 6, and so on until you can find a number that does. In this case 23 is the 1st and only number that divides evenly. In fact 23 is the sq rt of 529 and that is the answer.

In the case of sq rt of 1024 however it is easier to break down. The sq rt of 1024 = Sq rt of 2 x 512 = Sq rt of 2x2x256 = Sq rt of 2x2x2x128 = Sq rt of 2x2x2x2x64 = Sq rt of 16 x 64. Both 16 and 64 are easily recognized as 4 squared and 8 squared. So what you end up with is 4 x 8 = 32, which ultimately is the square root of 1024.

Answer 3

Assuming you can do long division [some of the answers assume you cannot because you asked how to do this manually], then I will assume you can do "short division" and do some short division in your head *and* that you know the basic properties of arithmetic. Given these assumptions, your question becomes 'is there an easy way to divide numbers?' An good answer for this type of problem is to make the division easier by: > finding a number N that is near the value of the numerator and > find a smaller number S to subtract from N so that the difference is the original value > then divide the two numbers, S and N, by the denominator to get the answer. This is how it would work for this example: 7.5/8 = (8-0.5)/8 = 8/8 - 0.5/8 = 1 - [1/2]/8 and 1/2 divided by 8 = 1/16. this may not seem easier [yet] but notice that 1/2 = 0.5 and half of that is 1/4 = 0.25 1/8 = 0.125, and finally 1/16 = 0.0625 SO, subtract the 0.0625 from 1 (can be done mentally with some care) to get 0.9375. **** Another easy way also depends on the numbers involved. In this case, note that 8 = 2*2*2 So? This means you can do simple divisions to the numerator (may be easy or not) and get the answer directly, i.e., 7.5/2 = 3.75; 3.75/2 = 1.875, and 1.875/2 = 0.9375 **** Finally, note that 8 * 10 = 80 and 80 / 4 = 80/(2*2) = 20 and 20 * 5 = 100. This means you can do the same multiplications and divisions to the numerator (may be easy or not) and get the answer. **** extra note: The easy way to add or subtract fractions is to note that you want each pair of digits to add up to 9 except the last pair should add up to 10. In this case, to add up the digits of the fraction of 0.0625 to 9 the numbers would be 9, 3, 7, and the last pair to add to 10 would be a 5. try it...

Answer 4

Factor them:

529 = 23^2 so sqrt(529) = 23 (you're not gonna know that one unless you memorize it or keep trying different factors)

1024 = 2^10 (I know it by memory xD) so sqrt(1024) = 2^5 = 32

Answer 5

Ok first you see what perfect square number goes into that

For example

√108
Now we find out the highest perfect square number which is 36

√36 x 3

now give them there own square root

√36 x √3

Find the square root of √36 which is 6
so

6 x √3

=

6√3

Answer 6

Memorize them. I knew those two without thinking, 23 and 32.

Steps:
The square root of a number is just the number which when multiplied by itself gives the first number. So 2 is the square root of 4 because 2 * 2 = 4.
http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html
(2.3 x 2.3 = 5.29) (3.2 x 3.2 = 10.24)

Answer 7

Hint:

They are both perfect squares

Hint #2:

1024 = 2^10

Answer 8

in your question
1024 is clearly divisible by 2
so go on factorising by 2
you will see that 1024 = 2^10

so √1024 = 2^5 = 32

another long division method is available at the following link

http://rbmix.com/math/squareroot/sqrt.php

Answer 9

getting the square root is simple

think of perfect squares
than you look at the number which is inbetween and then you get the answer if it is closer to the other root estimate to that answer

and vice versa

Answer 10

http://en.wikipedia.org/wiki/Methods_of_computing_square_roots