√385
385 is not a perfect square number, but it is too close to 400 so that its square root would be close to 20, that is ≥ 19.5...
To find it more precisely, you need to work a little bit.
√385 = 19. ...
1. 19; double 1 so 19 becomes 29.
2. 29*9 = 261, subtract it from 285 (385 - 100).
285 - 261 = 24, add 2 zeros to 24; 2400 (we add pairs of zeros after the decimal point)
2. 29; double 9, so 29 becomes 38
Now think for a number that will multiply 38_ so that the product to be close to 2400
386*6 = 2316 and 2400 - 2316 = 84, add 2 zeros to 84; 8400
√385 = 19.6 ...
3. 386; double 6, so 386 becomes 392
Now think for a number that will multiply 392_ so that the product to be close to 8400
3922*2 = 7844 and 8400 - 7844 = 556, add 2 zeros to 556; 55600
√385 = 19.62 ...
If you want more numbers, repeat doing the same thing continuously.
Chat with our AI personalities
The answer is 961. The square root of 961 is 31, which is a prime number.
You look for the largest perfect square, and take it out. In this case: root(125) = root(25 x 5) = root(25) x root(5) = 5 x root(5).
Take out the largest perfect square you can find, in this case, 4: root(40) = root(4 x 10) = root(4) x root(10) = 2 x root(10).
There are infinitely many of them. They include square root of (4.41) square root of (4.42) square root of (4.43) square root of (4.44) square root of (4.45) square root of (5.3) square root of (5.762) square root of (6) square root of (6.1) square root of (6.2)
Find the largest square that is a factor. That's 100. THe answer will be 10 times the square root of 2. √200 = √2 x 100 = √2 x √100 = 10√2