Is the square root of 200
The square root of 200 is approximately 14.1421356237.
To find the square root of 200 step-by-step, we can use the prime factorization method:
1. First, we need to find the prime factorization of 200:
- 200 divided by 2 equals 100.
- 100 divided by 2 equals 50.
- 50 divided by 2 equals 25.
- 25 is a perfect square, so we can stop here.
2. Now, we can rewrite 200 using its prime factorization: 200 = 2^3 * 5^2.
3. To find the square root of 200, we can rewrite it as the product of the square roots of its prime factors:
- The square root of 2^3 is √2^3 = 2^(3/2).
- The square root of 5^2 is √5^2 = 5^(2/2) = 5.
4. Finally, we can simplify the expression:
√200 = 2^(3/2) * 5 = 2√2 * 5 = 10√2.
Therefore, the square root of 200 is 10√2.
To find the square root of 200, you can follow these steps:
1. Start by making an educated guess. Since 200 falls between the perfect squares of 144 (12^2) and 225 (15^2), a reasonable guess would be that the square root of 200 is between 12 and 15.
2. Use a method like the Babylonian method or long division to refine your estimate. Let's use the Babylonian method:
i. Start by taking the guess you made in step 1 and divide the original number (200) by it. In this case, divide 200 by 12: 200 / 12 = 16.67.
ii. Next, find the average of the guess and the result of the division. Add your initial guess (12) to the result (16.67) and divide by 2: (12 + 16.67) / 2 = 14.34.
iii. Repeat steps i and ii using the new estimate obtained from step ii, until you achieve the desired level of accuracy. In this case, you could keep repeating steps i and ii until you are satisfied with the result.
3. Eventually, you will find that the square root of 200 is approximately 14.14.