Question

find the
$\sqrt{} 1024$
​

Answer 1

Answer:

32

Step-by-step explanation:

Here we will show you how to calculate the square root of 1024 using the long division method. This is the lost art of how they calculated the square root of 1024 by hand before modern technology was invented.

Step 1)

Set up 1024 in pairs of two digits from right to left:

10 24

Step 2)

Starting with the first set: the largest perfect square less than or equal to 10 is 9, and the square root of 9 is 3. Therefore, put 3 on top and 9 at the bottom like this:

3  

10 24

9    

Step 3)

Calculate 10 minus 9 and put the difference below. Then move down the next set of numbers.

3    

10 24

9    

1 24    

Step 4)

Double the number in green on top: 3 × 2 = 6. Then, use 6 and the bottom number to make this problem:

6? × ? ≤ 124

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 2. Replace the question marks in the problem with 2 to get:

62 × 2 = 124.

Now, enter 2 on top, and 124 at the bottom:

3 2  

10 24

9    

1 24    

1 24    

The difference between the bottom two numbers is zero, therefore, you are done! The answer is the green numbers on top. Once again, the square root of 1024 is 32.

Answer 2

Answer:

1024=2×2×2×2×2×2×2×2×2×2

_/1024=_/2×2×2×2×2×2×2×2×2×2

_/1024=2×2×2×2×2

_/1024=32