Is there a fast trick to find the squeare root of a number?

Question

Ex is there a fat way i can find the squeare root of 567???

And please dont say calculator

also, can you you show ways for perfect squeares too??

Answer 1

Finding square roots of of numbers that aren't perfect squares without a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.


Example: Calculate the square root of 10 to 2 decimal places.

1. Find the two perfect square numbers it lies between.


Solution:
32 = 9 and 42 = 16, so lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

Answer 2

The easiest way I can think of is to break it down into factors and then go from there. For example:

√567 = √(81 * 7) = 9√7.

Answer 3

There are several methods. The most accurate method is also tedious. I cannot remember it. Oddly I remember a few of the inaccurate ones. You can use algebra or arithmetic. Good luck! The quickest would depend upon your practice and preference.

Answer 4

The answer to your question is no, there`s not. Apart from the methods outlined above, you could calculate it by logs, or use the method of arithmetic extraction, which is complex and tedious.

Answer 5

Bisection:


try 20 x 20 = 400
try 25 x 25 = 625
try 24 * 24 = 576
try 23.7 * 23.7 = 561.69
try 23.8 * 23.8 =566.44
add a lil bit more 23.81*23.81 = 566.9 ~= 567

hence 23.81