how do you get the approximated square of a non-perfect square number?

Answer 1

Think or find the square root of the perfect number previous non-perfect and the square root of perfect number next of non-perfect number.
Example
find the square root of 23
16<23<25
sqrt(16) 4< sqrt(23) <5
answer: the square root of 23 is between 4 and 5

Answer 2

I think what you're asking is: "how do I approximate the square root of a number that isn't a perfect square?"

There are actually many different ways. (There are also ways to calculate square roots to whatever decimal precision you want, but that's a different question. :-) ) Here's one way.

Step 1: Find the closest number that *is* a perfect square. Figure out the difference between your number and that perfect square -- let's call that difference d.
Step 2: Take the square root of that perfect square number -- let's call that square root N.
Step 3: Divide d by (2*N), and either add or subtract that result from N (depending on whether your original number was greater or less than the perfect square).

The closer your original number is to the perfect square you choose, the closer your approximation will be to the real answer.

Here are two examples.

Example 1: Approximate the square root of 39. (The actual square root of 39 is about 6.245.)
Step 1: 36 is a perfect square. 39 - 36 = 3. Set d = 3.
Step 2: The root of 36 is 6. Set N = 6.
Step 3: d / (2 * N) = 3 / 12 = 0.25, and 6 + 0.25 = 6.25. Not bad.

Example 2: Approximate the square root of 117. (The actual root of 125 is about 10.817.)
Step 1: 121 is a perfect square, so set d = 121-117 = 4.
Step 2: The root of 121 is 11. Set N = 11.
Step 3: d / (2 * N) = 4 / 22 = 0.1818181818... and 11 - 0.181818... = 10.818181... which is, again, a pretty good approximation.

On the 2nd example, if we'd used 100 instead of 121 as our perfect square, then d = 117-100 = 17, N = 10, d / (2 * N) = 0.85, and 10 + 0.85 = 10.85, which is an okay approximation but not nearly as close, so when possible, try to use the closest perfect square, even if that means you have to subtract instead of add.

Hope that helps!

Answer 3

Firstly, you can get the answer from calculator.
Secondly, there is a nice method like long division with following steps:
* Starting from decimal point, pair off the digits.
* Take the leftmost pair; find what squared is just less than the given number made of the pair of digits; write it as if you are writing the quotient of a long division.
* Just as in long div, write the squared number below the leftmost pair and do subtraction
* Bring down the next (leftmost) pair, as you would do in a div.
* Bring down twice the "quotient", and find what digit added to it on its right, multiplied by that digit, gives a number just less than required.
* go on till the end or stop at any desired stage and fill with zero for every remaining pair and the decimal point at its proper place.

The method is fairly easy to do and not as complicated as it looks. But you know you have to write a whole page to explain how to tie shoe lace!

Answer 4

Newton-Raphson method works well.

For example:

Square root of 5 means that:

x^2-5=0

The derivative of that equation is 2x. (Power law of differentiation: bring the exponent down in front, subtract one from the power - i.e. 2 x^(2-1) or 2 x^1 or 2x)

You make a guess, say 2.

2^2-5=0? No, it equals -1. -1 is the amount of error in your guess. To adjust your guess, subtract the amount of error by the derivative, or

Guess 2 = 2 - (-1/2x). x was 2, so the answer is: 2+1/4 = 2.25

2.25^2-5=0? No, it equals about 5.06 (5.0625 to be exact, but if you had a calculator, you wouldn't need Newton's method). Your error is about 0.06

Guess 3 = 2.25 - [0.06/(2*2.25)] = 2.24

2.24^2 - 5 = 0? Not quite. It's around 5.01.

Repeat until you get the desired level of accuracy.

Answer 5

Do you mean the approximated square root?

Answer 6

You can find the square, cube, etc. or root, cubed root, etc. of any number by using the logarthmic tables. Eg. For cubed root of 81, you find log 81 to base 10, and then divide by 3, and then find the antilog. Eg. For 3^3 (3 to power of 3), you find log 3 to base 10, and then multiply by 3, and then find the antilog. Please try and verify.

Answer 7

Without using a calculator, iyiogrenci has the best answer thus far. That's how I'd do it, and that's how they've been doing it for centuries.

Answer 8

if your on a calculator you can use the button that looks like a dividing sign but with a check mark on the end of it

Answer 9

Round up or down a decimal place.

Answer 10

I suggest that you use the application of differential calculus