Find the square root of 512: 3√512
The square root of 512 is 22.63.
Nope try again
Apologies for the confusion. Let's try again.
To find the square root of 512, we can break it down as follows:
Since 512 = 8 * 64, we can simplify the square root as:
√512 = √(8 * 64)
Using the property of square roots: √(a * b) = √a * √b
√(8 * 64) = √8 * √64
Now, 8 can be written as 2 * 4:
√8 * √64 = √(2 * 4) * √64
Using the property of square roots again: √(a * b) = √a * √b
√(2 * 4) * √64 = √2 * √4 * √64
Now, we can solve for each term:
√2 * √4 * √64 = √2 * 2 * 8
Simplifying further:
√2 * 2 * 8 = 4√2 * 8
Finally:
4√2 * 8 = 32√2
Therefore, the square root of 512 is 32√2.
To find the square root of 512, the most common method is to use a calculator or a mathematical software program. However, if you want to find the simplified square root of 512 manually, you can follow these steps:
Step 1: Prime Factorization
Express 512 as a product of its prime factors:
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^9
Step 2: Simplify the Square Root
Take out pairs of the same prime factors from under the square root, leaving one factor of 2 remaining for each pair:
√512 = √(2^9) = 2^4√2
Step 3: Simplify the Remaining Factors
Evaluate the square root of the remaining factor:
2^4√2 = 16√2
So the square root of 512 is 16√2, which is approximately equal to 22.63.