Express the result in the simplest form 8 root 512
well, 512 = 2*16^2, so ...
To express the result in the simplest form, we need to simplify the square root.
First, we can simplify the number under the square root by finding the largest perfect square that divides evenly into 512. The largest perfect square that divides evenly into 512 is 64 (since 64 * 8 = 512).
So, we can rewrite 512 as (64 * 8).
Now, we can simplify the square root of 64, which is 8.
Therefore, the simplified result is 8 multiplied by the square root of 8, which can be written as 8√8.
To express the result in the simplest form, we need to simplify the square root of 512. Here's how we do it:
Step 1: Prime factorize 512:
512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
Step 2: Group the factors in pairs:
512 = (2 * 2) * (2 * 2) * (2 * 2) * (2 * 2) * 2
Step 3: Rewrite as square root:
512 = 2^4 * 2^4 * 2^4 * 2^4 * 2
Step 4: Use the rule of exponents to combine the powers:
512 = 2^(4 + 4 + 4 + 4) * 2
Step 5: Simplify:
512 = 2^16 * 2
Step 6: Multiply the 2s together:
512 = 2^17
Therefore, the simplified form of 8√512 is 8√(2^17).
NOTE: The square root of a number can also be expressed as a fractional exponent. If you prefer, you could write the simplified form as 8 * (2^17)^(1/2).