How do you figure out a square root?

Answer 1

I think the perfect squares are easy, such as sq rt 25, or sqrt 81. Possibly you are trying to understand finding the square root of numbers that are not perfect squares.

Let's say your teacher asks you to find the square root of 8.

Using prime factorization you say 8 = 2^3 (2x2x2) If you can circle any exact two numbers, that you can pull out from under the radical, leave what's left under the radical sign.

sq rt 8 = 2 sqrt 2

here's a few more:
sq rt 12 (2x2x3) = 2 sqrt 3

sq rt 56 (2x2x2x7) = 2 sq rt 14

sq rt 63 (3x3x7) = 3 sqrt 7

sq rt 112 (2x2x2x2x7) = 4 sqrt 7

Hope that helps!

Answer 2

One technique you can use to find the square root of x is to use the fact that if k is an approximate value, then a better approximation is:
(1/2)(k + (x / k)).

Try cycling through that a few times on a calculator, and then compare the result with the one obtained from using the square root key.

Answer 3

Factor the number in the simpliest form (primary numbers). For example, if you want to get the square root of 256 you have to factor it. You will see that 256=2^8 and the square root of 2^8 is 2^4, as you know, which is equal to 16.

Answer 4

Divide number into groups of 2 digits (100 possibilities).
e.g. 12 34
Find the largest square root for the first pair, then subtract.
i.e. 3 x 3 = 9, 12 - 9 = 3.
Bring down next digit:
i.e. 33
Divide by double the previous root:
i.e. 33/6 = 5 remainder 3
Insert decimal point in partial answer:
i.e. 35.
Bring down next digit to remainder:
i.e. 34
Divide by double the previous root:
i.e. 34/70

Answer 5

There is an algorithm but it is difficult to explain. An easier approach is successive approximations. Guess. Divide the number you are taking root of by your guess. Average your answer with the guess. Make this your new guess. Continue till your average is the same as your guess or match for as many decimal places as you need

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Answer 6

you find it out by multiplying that number. The square root of 10 is 10x10

Answer 7

just do the x^ (1/2)

x being any positive number

Answer 8

whhat do you mean figure out ?

√9 = 3
use a calculator OR log tables OR slide rule etc

Answer 9

Here's my answer: http://img164.imageshack.us/img164/9958/sqrtmd7.jpg