Determine ³squre root 1000 by using prime factors
To find the square root of 1000 using prime factors, we first need to factorize 1000.
The prime factorization of 1000 is:
1000 = 2^3 * 5^3
Next, we can group the prime factors in pairs to find the square root:
√(2^3 * 5^3) = √(2^2 * 2 * 5^2 * 5)
Taking the square root of each pair of factors:
√(2^2) * √(2) * √(5^2) * √(5) = 2 * √2 * 5 * √5
Simplifying further:
2 * 5 * √(2 * 5) = 10√10
Therefore, the square root of 1000 is 10√10.