√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.
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
Look for the largest square number in its factors. The square root of 512 is equal to the square root of 2 times the square root of 256. The square root of 256 is 16. The square root of 512 simplifies to 16 times the square root of 2.
99 has two square roots: 9.949874 and -9.949874. 9.949874 is the largest.
The largest 3-digit number - not itself a perfect square - is 999. Calculate its square root, round the answer down, then square the answer again.
The answer is 961. The square root of 961 is 31, which is a prime number.
385 hectares is 3,850,000 square meters.
961
No.
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).
9409
97969
The idea is to take out perfect squares. The largest perfect square in this case is 256, which is the square of 16 (if you have trouble figuring this out, you can take out a smaller perfect square first, and then see if you find additional perfect squares). In any case, the end result should not have a factor that is a perfect square. Using the symbol "root()" for square root: root(512) = root(256 x 2) = root(256) x root(2) = 16 root(2)